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Lumley Castle Hotel in County Durham
Categories: Places to stay 19 September 2020
Stuart Forster reviews a stay at Lumley Castle Hotel in Chester-le-Street, County Durham.
Like the idea of a stay in an English castle? It's possible at the Lumley Castle Hotel, a four-star property with a state-of-the-art escape room and a restaurant serving modern British cuisine.
England's north-east is dotted with castles. They stand as a legacy of turbulent times centuries ago when English and Scottish forces clashed frequently. Lumley Castle was constructed from 1389 for Sir Ralph Lumley, who just a year earlier had been taken prisoner by Scots while fighting at the Battle of Otterburn.
Three centuries ago, the castle underwent renovations by one of England's most celebrated architects, Sir John Vanbrugh. It later became a residence of the Bishop of Durham and has been utilised as place of learning by Durham University. In 1976 the Grade I listed building opened as a hotel, presenting guests with opportunities to stay overnight in a castle.
The Sir John Vanbrugh-designed wing, dating from the 1720s, at Lumley Castle in County Durham.
Rooms at Lumley Castle Hotel
Lumley Castle Hotel has a total of 73 guestrooms in seven categories. They range from Courtyard Classic rooms, in the converted stable block adjacent to the castle, to the King James Suite. The suite is named after King James I of England who stayed in the castle in 1603, the first year of his reign.
Accompanied by my partner, I spent a night in one of the Courtyard State rooms. Comfortable and spacious, the classically furnished room featured a four-poster bed and Nespresso coffee making machine. Framed prints of woodcuts depicting characters from British history, including Mary Queen of Scots and Oliver Cromwell, hung in the bedroom and bathroom.
The bathroom featured a bathtub and shower. It was stocked with Bulgari toiletries and bathrobes hung in the wardrobe.
Four-poster bed and armchairs in one of the Courtyard State rooms at Lumley Castle Hotel in County Durham.
Food at Lumley Castle hotel
Lumley Castle's Knights Restaurant and Library Bar underwent refurbishment early in 2020. The lengthy closure of British hospitality venues, due to the coronavirus pandemic, means that many locals are yet to visit and experience what they can offer since reopening. Dinner sittings are from 6.30pm.
Prior to dinner, we were shown to seats in the bar to peruse the menu over drinks. I opted for a classic gin-based Bramble rather than one of the seasonal cocktails. Impressed by the mixologist's work, I ordered a second.
Cured and torched mackerel with caviar served with a salad featuring tomato and basil at the Knights Restaurant.
The dining concept is based around a comfortable interpretation of a cathedral-style refectory with handcrafted pottery. The vaulted arching of the restaurant's ceiling is a natural fit.
Executive chef Craig Sherrington has developed a modern menu incorporating locally sourced ingredients and regional dishes such as Northumberland vegetable broth and roast Lakeland lamb.
Onion bhaji made with spring onion served with a smoked cheese sauce.
A beautifully present starter
The cured and torched mackerel proved a beautifully presented starter. Following our server's recommendation, we also ordered a spring onion bhaji. Served with a smoked cheese sauce, the lightly spiced bhaji was impressively flavoursome and succulent.
The choice of mains included blackened salmon and braised pork belly but neither of us looked beyond the temptation of a rib eye steak. The 28-day aged steaks were served with a roast tomato and a flavour-packed field mushroom plus a choice of two side dishes.
Rib eye steak served with field mushroom, grilled tomato, chips and Bearnaise sauce in the Knights Restaurant.
To accompany the steaks we selected two glasses of the Châteauneuf-du-Pape Réserve des Argentiers from the hotel's Priority Wine List. Its options are served in sizes from 125-millilitre glasses upwards.
Service in the Knights Restaurant was attentive and the food enjoyable.
Eggs Benedict served for breakfast.
Measures to combat Covid-19
The pandemic is having a major impact on leisure travel and businesses in the hospitality industry. With people favouring staycations over holidays abroad, hotels in north-east England may be able to attraction clients who normally favour far-flung destinations for weekend breaks.
Reassuringly, Lumley Castle Hotel has introduced visible measures to minimise the risk of infection during the coronavirus pandemic. A one-way route has been introduced in corridors. Face masks are provided and wearing them is mandatory while walking along corridors.
A view of the inner courtyard at Lumley Castle Hotel in north-east England.
While checking in, I noticed that the pens at the reception had been disinfected and placed in small bags.
One potential downside during the COVID-19 pandemic is that luggage is not being stored in the hotel. The capacity of the restaurant and bar have also been cut.
Exterior of Lumley Castle, one of the castle hotels in England.
A stroll through the hotel
The first photograph that I ever developed (on film, in a darkroom) was of one of the Roman-style busts in one of the corridors of the Lumley Castle Hotel. Many years on, I was pleased to see that the heads are still present. This time my photos were digital.
Roman-style heads in one of the hotel's corridors.
According to legend, the woman who had a relationship with Sir Ralph Lumley before his marriage was bundled down a well by priests. The ghost of Lily of Lumley is reputed to haunt the castle. She features as a character in the escape room, which lays claim to being the first in any English castle.
I'm grateful to general manager Gordon Cartwright for taking the time to walk us through the grand function rooms usually used during wedding receptions and corporate events at Lumley Castle Hotel.
The castle proved a pleasant base for a romantic night away with dinner.
Bas relief detail on the walls and ceiling of one Lumley Castle's function rooms.
Things to do near Lumley Castle Hotel
Lumley Castle is ideally placed if you're looking for a base to attend a cricket match at the Durham Riverside ground. The ground, where England won the Ashes in 2013, is less than a mile from the hotel.
The footpaths of Chester-le-Street's Riverside Park are well-suited for a relaxing stroll or run. A five-kilometre parkrun takes place each Saturday morning at 9.00am. The park is across the other side of the River Wear to the hotel.
Play golf? Chester-le-Street Golf Club is next to Lumley Castle Hotel. The two collaborate to offer morning tee times to guests staying at the hotel. The 18-hole course was laid out in the early part of the last century to a design by two Open Championship winners.
A pergola in the outer courtyard of the Lumley Castle Hotel, an option for people seeking accommodation in hotels in northeast England.
A market is held in Chester-le-Street on Fridays and Saturdays.
From Chester-le-Street it's a 15 minute drive to Durham City, less than eight miles to the south. It takes five minutes on a train to get to Durham, whose UNESCO World Heritage Site castle and cathedral count as the headline attractions.
Another option is to park at the foot of Penshaw Hill, six miles away, and visit Penshaw Monument. Reminiscent of a Greek temple, the National Trust-operated memorial to the Earl of Durham counts among reasons to visit Sunderland.
Newcastle upon Tyne, 11 miles from Chester-le-Street, is an eight-minute journey by train. Known for its nightlife, Newcastle has several museums and art galleries that warrant visiting.
Tower of Lumley Castle, dating from 1389, in north-east England.
See the Lumley Castle Hotel (Ropery Lane, Chester-le-Street, DH3 4NX; tel. 0191 389 1111) website for more information about the hotel, castle's history and rooms. The website also has information about the Lumley Castle afternoon tea, weddings at the castle, special offers and events such as whisky tastings.
Interested in getting a good deal for a weekend break? Registering for membership of the Lumley Castle Priority Club provides access to offers including discounted stays and meals. It also means being able to select wines from the Priority Wine List while dining in the hotel's Knights Restaurant.
The escape room at Lumley Castle Hotel can be booked for between two and six players.
Lumley Castle Hotel has free onsite parking and free access to wi-fi.
Take a look at the This is Durham website for more information about things to do in County Durham.
Photos illustrating this post are by Why Eye Photography, which is available for to undertake travel and food photography shoots across north-east England and beyond.
Use Pinterest? Pin this and share Go Eat Do's blog post about staying at Lumley Castle Hotel and dining at the Knights Restaurant in Chester-le-Street, County Durham.
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Walking at Castle Eden Dene in County Durham | Go Eat Do
November 7, 2020 at 12:02 Reply
[…] County Durham? The highly rated Seaham Hall hotel and spa is a 20-minute drive north of the dene. Lumley Castle Hotel is 30 minutes' drive […]
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// Licensed to the Apache Software Foundation (ASF) under one
// or more contributor license agreements.  See the NOTICE file
// distributed with this work for additional information
// regarding copyright ownership.  The ASF licenses this file
// to you under the Apache License, Version 2.0 (the
// "License"); you may not use this file except in compliance
// with the License.  You may obtain a copy of the License at
//
//   http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing,
// software distributed under the License is distributed on an
// "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.  See the License for the
// specific language governing permissions and limitations
// under the License.

//! ExecutionContext contains methods for registering data sources and executing SQL queries

use std::cell::RefCell;
use std::collections::HashMap;
use std::rc::Rc;
use std::string::String;
use std::sync::Arc;

use arrow::datatypes::*;

use crate::datasource::csv::CsvFile;
use crate::datasource::datasource::Table;
use crate::dfparser::{DFASTNode, DFParser};
use crate::execution::aggregate::AggregateRelation;
use crate::execution::error::{ExecutionError, Result};
use crate::execution::expression::*;
use crate::execution::filter::FilterRelation;
use crate::execution::limit::LimitRelation;
use crate::execution::projection::ProjectRelation;
use crate::execution::relation::{DataSourceRelation, Relation};
use crate::logicalplan::*;
use crate::optimizer::optimizer::OptimizerRule;
use crate::optimizer::projection_push_down::ProjectionPushDown;
use crate::sqlplanner::{SchemaProvider, SqlToRel};

pub struct ExecutionContext {
    datasources: Rc<RefCell<HashMap<String, Rc<Table>>>>,
}

impl ExecutionContext {
    /// Create a new excution context for in-memory queries
    pub fn new() -> Self {
        Self {
            datasources: Rc::new(RefCell::new(HashMap::new())),
        }
    }

    /// Execute a SQL query and produce a Relation (a schema-aware iterator over a series
    /// of RecordBatch instances)
    pub fn sql(&mut self, sql: &str, batch_size: usize) -> Result<Rc<RefCell<Relation>>> {
        let plan = self.create_logical_plan(sql)?;
        Ok(self.execute(&plan, batch_size)?)
    }

    /// Creates a logical plan
    pub fn create_logical_plan(&mut self, sql: &str) -> Result<Arc<LogicalPlan>> {
        let ast = DFParser::parse_sql(String::from(sql))?;

        match ast {
            DFASTNode::ANSI(ansi) => {
                let schema_provider: Arc<SchemaProvider> =
                    Arc::new(ExecutionContextSchemaProvider {
                        datasources: self.datasources.clone(),
                    });

                // create a query planner
                let query_planner = SqlToRel::new(schema_provider);

                // plan the query (create a logical relational plan)
                let plan = query_planner.sql_to_rel(&ansi)?;

                Ok(self.optimize(&plan)?)
            }
            _ => unimplemented!(),
        }
    }

    /// Register a CSV file as a table so that it can be queried from SQL
    pub fn register_csv(
        &mut self,
        name: &str,
        filename: &str,
        schema: &Schema,
        has_header: bool,
    ) {
        self.register_table(name, Rc::new(CsvFile::new(filename, schema, has_header)));
    }

    /// Register a table so that it can be queried from SQL
    pub fn register_table(&mut self, name: &str, provider: Rc<Table>) {
        self.datasources
            .borrow_mut()
            .insert(name.to_string(), provider);
    }

    /// Optimize the logical plan by applying optimizer rules
    fn optimize(&self, plan: &LogicalPlan) -> Result<Arc<LogicalPlan>> {
        let mut rule = ProjectionPushDown::new();
        Ok(rule.optimize(plan)?)
    }

    /// Execute a logical plan and produce a Relation (a schema-aware iterator over a series
    /// of RecordBatch instances)
    pub fn execute(
        &mut self,
        plan: &LogicalPlan,
        batch_size: usize,
    ) -> Result<Rc<RefCell<Relation>>> {
        match *plan {
            LogicalPlan::TableScan {
                ref table_name,
                ref projection,
                ..
            } => match self.datasources.borrow().get(table_name) {
                Some(provider) => {
                    let ds = provider.scan(projection, batch_size)?;
                    if ds.len() == 1 {
                        Ok(Rc::new(RefCell::new(DataSourceRelation::new(
                            ds[0].clone(),
                        ))))
                    } else {
                        Err(ExecutionError::General(
                            "Execution engine only supports single partition".to_string(),
                        ))
                    }
                }
                _ => Err(ExecutionError::General(format!(
                    "No table registered as '{}'",
                    table_name
                ))),
            },
            LogicalPlan::Selection {
                ref expr,
                ref input,
            } => {
                let input_rel = self.execute(input, batch_size)?;
                let input_schema = input_rel.as_ref().borrow().schema().clone();
                let runtime_expr = compile_scalar_expr(&self, expr, &input_schema)?;
                let rel = FilterRelation::new(
                    input_rel,
                    runtime_expr, /* .get_func().clone() */
                    input_schema,
                );
                Ok(Rc::new(RefCell::new(rel)))
            }
            LogicalPlan::Projection {
                ref expr,
                ref input,
                ..
            } => {
                let input_rel = self.execute(input, batch_size)?;

                let input_schema = input_rel.as_ref().borrow().schema().clone();

                let project_columns: Vec<Field> =
                    exprlist_to_fields(&expr, &input_schema);

                let project_schema = Arc::new(Schema::new(project_columns));

                let compiled_expr: Result<Vec<RuntimeExpr>> = expr
                    .iter()
                    .map(|e| compile_scalar_expr(&self, e, &input_schema))
                    .collect();

                let rel = ProjectRelation::new(input_rel, compiled_expr?, project_schema);

                Ok(Rc::new(RefCell::new(rel)))
            }
            LogicalPlan::Aggregate {
                ref input,
                ref group_expr,
                ref aggr_expr,
                ..
            } => {
                let input_rel = self.execute(&input, batch_size)?;

                let input_schema = input_rel.as_ref().borrow().schema().clone();

                let compiled_group_expr_result: Result<Vec<RuntimeExpr>> = group_expr
                    .iter()
                    .map(|e| compile_scalar_expr(&self, e, &input_schema))
                    .collect();
                let compiled_group_expr = compiled_group_expr_result?;

                let compiled_aggr_expr_result: Result<Vec<RuntimeExpr>> = aggr_expr
                    .iter()
                    .map(|e| compile_expr(&self, e, &input_schema))
                    .collect();
                let compiled_aggr_expr = compiled_aggr_expr_result?;

                let mut output_fields: Vec<Field> = vec![];
                for expr in group_expr {
                    output_fields.push(expr_to_field(expr, input_schema.as_ref()));
                }
                for expr in aggr_expr {
                    output_fields.push(expr_to_field(expr, input_schema.as_ref()));
                }
                let rel = AggregateRelation::new(
                    Arc::new(Schema::new(output_fields)),
                    input_rel,
                    compiled_group_expr,
                    compiled_aggr_expr,
                );

                Ok(Rc::new(RefCell::new(rel)))
            }
            LogicalPlan::Limit {
                ref expr,
                ref input,
                ..
            } => {
                let input_rel = self.execute(input, batch_size)?;

                let input_schema = input_rel.as_ref().borrow().schema().clone();

                match expr {
                    &Expr::Literal(ref scalar_value) => {
                        let limit: usize = match scalar_value {
                            ScalarValue::Int8(x) => Ok(*x as usize),
                            ScalarValue::Int16(x) => Ok(*x as usize),
                            ScalarValue::Int32(x) => Ok(*x as usize),
                            ScalarValue::Int64(x) => Ok(*x as usize),
                            ScalarValue::UInt8(x) => Ok(*x as usize),
                            ScalarValue::UInt16(x) => Ok(*x as usize),
                            ScalarValue::UInt32(x) => Ok(*x as usize),
                            ScalarValue::UInt64(x) => Ok(*x as usize),
                            _ => Err(ExecutionError::ExecutionError(
                                "Limit only support positive integer literals"
                                    .to_string(),
                            )),
                        }?;
                        let rel = LimitRelation::new(input_rel, limit, input_schema);
                        Ok(Rc::new(RefCell::new(rel)))
                    }
                    _ => Err(ExecutionError::ExecutionError(
                        "Limit only support positive integer literals".to_string(),
                    )),
                }
            }

            _ => unimplemented!(),
        }
    }
}

/// Create field meta-data from an expression, for use in a result set schema
pub fn expr_to_field(e: &Expr, input_schema: &Schema) -> Field {
    match e {
        Expr::Column(i) => input_schema.fields()[*i].clone(),
        Expr::Literal(ref lit) => Field::new("lit", lit.get_datatype(), true),
        Expr::ScalarFunction {
            ref name,
            ref return_type,
            ..
        } => Field::new(&name, return_type.clone(), true),
        Expr::AggregateFunction {
            ref name,
            ref return_type,
            ..
        } => Field::new(&name, return_type.clone(), true),
        Expr::Cast { ref data_type, .. } => Field::new("cast", data_type.clone(), true),
        Expr::BinaryExpr {
            ref left,
            ref right,
            ..
        } => {
            let left_type = left.get_type(input_schema);
            let right_type = right.get_type(input_schema);
            Field::new(
                "binary_expr",
                get_supertype(&left_type, &right_type).unwrap(),
                true,
            )
        }
        _ => unimplemented!("Cannot determine schema type for expression {:?}", e),
    }
}

/// Create field meta-data from an expression, for use in a result set schema
pub fn exprlist_to_fields(expr: &Vec<Expr>, input_schema: &Schema) -> Vec<Field> {
    expr.iter()
        .map(|e| expr_to_field(e, input_schema))
        .collect()
}

struct ExecutionContextSchemaProvider {
    datasources: Rc<RefCell<HashMap<String, Rc<Table>>>>,
}
impl SchemaProvider for ExecutionContextSchemaProvider {
    fn get_table_meta(&self, name: &str) -> Option<Arc<Schema>> {
        match self.datasources.borrow().get(name) {
            Some(ds) => Some(ds.schema().clone()),
            None => None,
        }
    }

    fn get_function_meta(&self, _name: &str) -> Option<Arc<FunctionMeta>> {
        unimplemented!()
    }
}

redpajama_set_name: RedPajamaGithub


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Q: How to solve the the Curl's "Couldn't connect to server" I'm using Rspec with Capybara with WebMock for my tests (also I'm using Charles proxy), Getting the following error, never in a specific test.
I've had this happen once in a while, using rspec-retry mostly to deal with it, but now I've noticed it take allot of time on each encounter with this error.
Any ideas?
    Curl::Err::ConnectionFailedError: Couldn't connect to server
    /home/user/.rvm/gems/ruby-2.2.4/gems/curb-0.8.8/lib/curl/easy.rb:72:in `perform'
    /home/user/.rvm/gems/ruby-2.2.4/gems/curb-0.8.8/lib/curl/easy.rb:294:in `http'
    /home/user/.rvm/gems/ruby-2.2.4/gems/curb-0.8.8/lib/curl/easy.rb:294:in `http_get'
    /home/user/.rvm/gems/ruby-2.2.4/gems/selenium-webdriver-2.53.4/lib/selenium/webdriver/remote/http/curb.rb:63:in `request'
    /home/user/.rvm/gems/ruby-2.2.4/gems/selenium-webdriver-2.53.4/lib/selenium/webdriver/remote/http/common.rb:59:in `call'
    /home/user/.rvm/gems/ruby-2.2.4/gems/selenium-webdriver-2.53.4/lib/selenium/webdriver/remote/bridge.rb:649:in `raw_execute'
    /home/user/.rvm/gems/ruby-2.2.4/gems/selenium-webdriver-2.53.4/lib/selenium/webdriver/remote/bridge.rb:627:in `execute'
    /home/user/.rvm/gems/ruby-2.2.4/gems/selenium-webdriver-2.53.4/lib/selenium/webdriver/remote/bridge.rb:576:in `isElementDisplayed'
    /home/user/.rvm/gems/ruby-2.2.4/gems/selenium-webdriver-2.53.4/lib/selenium/webdriver/common/element.rb:190:in `displayed?'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/selenium/node.rb:126:in `visible?'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/element.rb:252:in `block in visible?'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/base.rb:81:in `synchronize'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/element.rb:252:in `visible?'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/queries/selector_query.rb:49:in `matches_filters?'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/result.rb:28:in `block in initialize'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/result.rb:28:in `select'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/result.rb:28:in `initialize'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/queries/selector_query.rb:120:in `new'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/queries/selector_query.rb:120:in `block in resolve_for'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/base.rb:81:in `synchronize'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/queries/selector_query.rb:108:in `resolve_for'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/matchers.rb:125:in `block in assert_selector'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/base.rb:85:in `synchronize'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/matchers.rb:124:in `assert_selector'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/matchers.rb:40:in `has_selector?'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/node/matchers.rb:271:in `has_css?'
    /home/user/.rvm/gems/ruby-2.2.4/gems/capybara-2.7.1/lib/capybara/session.rb:699:in `block (2 levels) in <class:Session>'
    ./spec/charts/charts_dialog_spec.rb:203:in `block in simple_chart_breakdown_initial'
    ./spec/charts/charts_dialog_spec.rb:201:in `times'
    ./spec/charts/charts_dialog_spec.rb:201:in `simple_chart_breakdown_initial'
    ./spec/charts/charts_dialog_spec.rb:1113:in `block (7 levels) in <top (required)>'
    /home/user/.rvm/gems/ruby-2.2.4/gems/rspec-retry-0.4.5/lib/rspec/retry.rb:98:in `block in run'
    /home/user/.rvm/gems/ruby-2.2.4/gems/rspec-retry-0.4.5/lib/rspec/retry.rb:88:in `loop'
    /home/user/.rvm/gems/ruby-2.2.4/gems/rspec-retry-0.4.5/lib/rspec/retry.rb:88:in `run'
    /home/user/.rvm/gems/ruby-2.2.4/gems/rspec-retry-0.4.5/lib/rspec_ext/rspec_ext.rb:12:in `run_with_retry'
    /home/user/.rvm/gems/ruby-2.2.4/gems/rspec-retry-0.4.5/lib/rspec/retry.rb:22:in `block (2 levels) in setup'
    -e:1:in `load'
    -e:1:in `<main>'

origianl Gemfile.lock:
    GEM
    remote: https://rubygems.org/
    specs:
    activesupport (4.2.5)
      i18n (~> 0.7)
      json (~> 1.7, >= 1.7.7)
      minitest (~> 5.1)
      thread_safe (~> 0.3, >= 0.3.4)
      tzinfo (~> 1.1)
    addressable (2.4.0)
    archive-zip (0.7.0)
      io-like (~> 0.3.0)
    backports (3.6.8)
    binding_of_caller (0.7.2)
      debug_inspector (>= 0.0.1)
    builder (3.2.2)
    capybara (2.7.1)
      addressable
      mime-types (>= 1.16)
      nokogiri (>= 1.3.3)
      rack (>= 1.0.0)
      rack-test (>= 0.5.4)
      xpath (~> 2.0)
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redpajama_set_name: RedPajamaStackExchange


text:
'Roll Up and Shine': A case study of Stereophonics at Glasgow's SECC arena
Emma Webster
School of Art, Media and American Studies
'You have to put as much effort into putting somebody on to 120 people as to putting them on to 2,000 people, almost. It's a bigger gamble, financially, but probably less work ... The bigger the act, it's probably less work' (S. Basford, pers. comm., 6 July 2009). So Sheffield-based promoter, Stuart Basford, concluded when considering his role within large-scale live music events, and whose somewhat surprising analysis will form the basis of this chapter. While promoters stand to lose or gain more at large shows than for smaller shows, both in terms of financial and reputational gain, their involvement at large shows such as arena concerts is often far from being anywhere like as hands-on. Hence the seemingly paradoxical statement that as the size and scale of the show increases, so too the promoter's active role decreases. Drawing on ethnographic research from a Stereophonics concert at the SECC arena in Glasgow in March 2010, this chapter will examine the multi-layered operation of an arena concert show such as the Stereophonics from the promoter's perspective. It will set out the role of the promoter, offer particular insights relating to the 'behind the scenes' activities at the Stereophonics show and finally consider what this means for the UK arena concert sector.
The Arena Concert
Music, Media and Mass Entertainment
Benjamin Halligan, Kirsty Fairclough-Isaacs, Robert Edgar, Nicola Spelman
Webster, E. (2015). 'Roll Up and Shine': A case study of Stereophonics at Glasgow's SECC arena. In B. Halligan, K. Fairclough-Isaacs, R. Edgar, & N. Spelman (Eds.), The Arena Concert: Music, Media and Mass Entertainment (pp. 114). Bloomsbury Academic.
Webster, Emma. / 'Roll Up and Shine': A case study of Stereophonics at Glasgow's SECC arena. The Arena Concert: Music, Media and Mass Entertainment. editor / Benjamin Halligan ; Kirsty Fairclough-Isaacs ; Robert Edgar ; Nicola Spelman. London : Bloomsbury Academic, 2015. pp. 114
@inbook{2691b6d77e0643699ee838298d301e00,
title = "{\textquoteleft}Roll Up and Shine{\textquoteright}: A case study of Stereophonics at Glasgow{\textquoteright}s SECC arena",
abstract = "{\textquoteleft}You have to put as much effort into putting somebody on to 120 people as to putting them on to 2,000 people, almost. It{\textquoteright}s a bigger gamble, financially, but probably less work ... The bigger the act, it{\textquoteright}s probably less work{\textquoteright} (S. Basford, pers. comm., 6 July 2009). So Sheffield-based promoter, Stuart Basford, concluded when considering his role within large-scale live music events, and whose somewhat surprising analysis will form the basis of this chapter. While promoters stand to lose or gain more at large shows than for smaller shows, both in terms of financial and reputational gain, their involvement at large shows such as arena concerts is often far from being anywhere like as hands-on. Hence the seemingly paradoxical statement that as the size and scale of the show increases, so too the promoter{\textquoteright}s active role decreases. Drawing on ethnographic research from a Stereophonics concert at the SECC arena in Glasgow in March 2010, this chapter will examine the multi-layered operation of an arena concert show such as the Stereophonics from the promoter{\textquoteright}s perspective. It will set out the role of the promoter, offer particular insights relating to the {\textquoteleft}behind the scenes{\textquoteright} activities at the Stereophonics show and finally consider what this means for the UK arena concert sector. ",
author = "Emma Webster",
editor = "Benjamin Halligan and Kirsty Fairclough-Isaacs and Robert Edgar and Nicola Spelman",
booktitle = "The Arena Concert",
publisher = "Bloomsbury Academic",
Webster, E 2015, 'Roll Up and Shine': A case study of Stereophonics at Glasgow's SECC arena. in B Halligan, K Fairclough-Isaacs, R Edgar & N Spelman (eds), The Arena Concert: Music, Media and Mass Entertainment. Bloomsbury Academic, London, pp. 114.
'Roll Up and Shine': A case study of Stereophonics at Glasgow's SECC arena. / Webster, Emma.
The Arena Concert: Music, Media and Mass Entertainment. ed. / Benjamin Halligan; Kirsty Fairclough-Isaacs; Robert Edgar; Nicola Spelman. London : Bloomsbury Academic, 2015. p. 114.
T1 - 'Roll Up and Shine': A case study of Stereophonics at Glasgow's SECC arena
AU - Webster, Emma
N2 - 'You have to put as much effort into putting somebody on to 120 people as to putting them on to 2,000 people, almost. It's a bigger gamble, financially, but probably less work ... The bigger the act, it's probably less work' (S. Basford, pers. comm., 6 July 2009). So Sheffield-based promoter, Stuart Basford, concluded when considering his role within large-scale live music events, and whose somewhat surprising analysis will form the basis of this chapter. While promoters stand to lose or gain more at large shows than for smaller shows, both in terms of financial and reputational gain, their involvement at large shows such as arena concerts is often far from being anywhere like as hands-on. Hence the seemingly paradoxical statement that as the size and scale of the show increases, so too the promoter's active role decreases. Drawing on ethnographic research from a Stereophonics concert at the SECC arena in Glasgow in March 2010, this chapter will examine the multi-layered operation of an arena concert show such as the Stereophonics from the promoter's perspective. It will set out the role of the promoter, offer particular insights relating to the 'behind the scenes' activities at the Stereophonics show and finally consider what this means for the UK arena concert sector.
AB - 'You have to put as much effort into putting somebody on to 120 people as to putting them on to 2,000 people, almost. It's a bigger gamble, financially, but probably less work ... The bigger the act, it's probably less work' (S. Basford, pers. comm., 6 July 2009). So Sheffield-based promoter, Stuart Basford, concluded when considering his role within large-scale live music events, and whose somewhat surprising analysis will form the basis of this chapter. While promoters stand to lose or gain more at large shows than for smaller shows, both in terms of financial and reputational gain, their involvement at large shows such as arena concerts is often far from being anywhere like as hands-on. Hence the seemingly paradoxical statement that as the size and scale of the show increases, so too the promoter's active role decreases. Drawing on ethnographic research from a Stereophonics concert at the SECC arena in Glasgow in March 2010, this chapter will examine the multi-layered operation of an arena concert show such as the Stereophonics from the promoter's perspective. It will set out the role of the promoter, offer particular insights relating to the 'behind the scenes' activities at the Stereophonics show and finally consider what this means for the UK arena concert sector.
BT - The Arena Concert
A2 - Halligan, Benjamin
A2 - Fairclough-Isaacs, Kirsty
A2 - Edgar, Robert
A2 - Spelman, Nicola
PB - Bloomsbury Academic
CY - London
Webster E. 'Roll Up and Shine': A case study of Stereophonics at Glasgow's SECC arena. In Halligan B, Fairclough-Isaacs K, Edgar R, Spelman N, editors, The Arena Concert: Music, Media and Mass Entertainment. London: Bloomsbury Academic. 2015. p. 114

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}

Conformal field theories in two dimensions have many applications in string theory and condensed-matter physics. In some applications the system under consideration, say strings in a given space-time, dictates the theory to be studied. In some other cases however, a CFT is used as a phenomelogical theory for a system without a known first-principles description. The relevant theory must then be chosen among the known CFTs according to the desired properties of the system. This approach relies on the existence of a large enough number of CFTs among which to choose, and on a good enough knowledge of their properties. Many rational CFTs are known, and their properties are often well-understood. However most CFTs are non-rational, and only a few non-rational CFTs have been solved so far, among them Liouville theory \cite{tes01a} and the $\Hp$ model \cite{gaw91}. It is therefore interesting to expand the small family of solvable non-rational CFTs.

The inspiration for the present article comes from the relation \cite{rt05} between the correlation functions of the $\Hp$ model and correlation functions of Liouville theory. Namely, correlators of generic $\Hp$ primary fields are related to correlators involving both generic Liouville primary fields, and the particular field $V_{-\frac{1}{2b}}$ where $b$ is related to the central charge of Liouville theory by $c=1+6(b+b^{-1})^2$. This field is known to be a degenerate field with a null vector at level two, which implies that Liouville correlators involving this field obey second-order differential equations \cite{bpz84}. But there is an infinite series of degenerate fields in Liouville theory, which lead to higher-order differential equations. It is therefore natural to wonder whether Liouville correlators involving such degenerate fields -- or even generic fields -- can be related to correlators in some models which would be generalizations of the $\Hp$ model.

We will propose a positive answer to this question, and sketch some properties of the resulting models. In contrast to the usual situation in the study of conformal field theory, we start with the solution of the models, namely an ansatz for their correlators in terms of Liouville correlators. The problem is then to reconstruct the models, and in particular their symmetry algebra, from their correlators. This is a priori a non-trivial problem, because our ansatz gives us only correlators of primary fields, but the notion of a primary field is not even defined if we do not know the symmetry algebra. Fortunately, the correct symmetry algebra will be suggested by the Lagrangian description of the models, which is very similar to the free-field description of the $\Hp$ model. (The new Lagrangians however do not correspond to sigma models.) We will then check that this symmetry algebra is consistent with the properties of the correlators, in particular in the case when they obey third-order differential equations.

\zeq\section{An ansatz for the correlation functions}

Our ansatz will be directly inspired by the $\Hp$-Liouville relation, we will therefore begin by a reminder of this relation. More details and references can be found in \cite{rt05}.

\subsection{Reminder of the $\Hp$-Liouville relation}

In the conformal bootstrap approach, the $\Hp$ model is defined by its symmetry algebra, and primary fields which transform in a certain way with respect to this algebra. Solving the model means finding the correlation functions of the primary fields; these correlation functions are subject to symmetry and consistency conditions. Let us briefly review these objects.
The chiral symmetry algebra of the $\Hp$ model is the affine Lie algebra $\asl$, which is generated by three currents $J^3(z),J^+(z),J^-(z)$ with the following operator product expansions (OPEs):
\bea
J^3(z)J^3(w) &=& -\frac{\frac{k}{2}}{(z-w)^2} + O(1)\ ,
\label{jtjt}
\\
J^3(z)J^\pm(w)&=& \pm \frac{J^\pm(w)}{z-w} + O(1)\ ,
\label{jtjpm}
\\
J^+(z)J^-(w) &=& -\frac{k}{(z-w)^2}+ \frac{2J^3(w)}{z-w}+ O(1)\ ,
\label{jpjm}
\eea
where $k>2$ is called the level of the affine Lie algebra. As a consequence, the $\Hp$ model is a conformal field theory with central charge $c=\frac{3k}{k-2}$; the stress-energy tensor which generates the conformal transformations can be deduced from the currents by the Sugawara construction \cite{fms97}
\bea
T = \frac{1}{2(k-2)}\left[ (J^+J^-)+(J^-J^+)-2(J^3J^3)\right]\ ,
\label{tjj}
\eea
where we use the following definition of the normal-ordered product of operators:
\bea
(AB)(z) =\frac{1}{2\pi i}\oint_z dx\ \frac{dx}{x-z}A(x)B(z)  \ .
\label{abz}
\eea
Affine primary operators $\Phi^j(\mu|w)$ with spin $j$, isospin $\mu$ and worldsheet position $w$ are defined by their OPEs with the currents, from which their OPEs with the stress-energy tensor follows:
\bea
J^-(z) \Phi^j(\mu|w) &=& \frac{\mu}{z-w} \Phi^j(\mu|w) + O(1)\ ,
\label{jmph}
\\
J^3(z) \Phi^j(\mu|w) &=& \frac{\mu\pp{\mu} }{z-w} \Phi^j(\mu|w) +O(1)\ ,
\label{jtph}
\\
J^+(z) \Phi^j(\mu|w) &=& \frac{\mu\ppd{\mu} -\frac{j(j+1)}{\mu}}{z-w}
\Phi^j(\mu|w) + O(1) \ ,
\label{jpph}
\\
T(z) \Phi^j(\mu|w) &=& \frac{\Delta_j}{(z-w)^2} \Phi^j(\mu|w) + \frac{1}{z-w}\pp{w} \Phi^j(\mu|w) +O(1) \ ,
\label{tph}
\eea
where the conformal dimension of the field $\Phi^j(\mu|w)$ is
\bea
\Delta_j = -\frac{j(j+1)}{k-2}\ .
\label{dj}
\eea
The fields $\Phi^j(\mu|w)$ have similar OPEs with the antiholomorphic currents $\bJ^a(\bz)$ and stress-energy tensor $\bar{T}(\bz)$, but their dependences on $\bz$ and $\bar{\mu}$ will be kept implicit.
The spin takes values $j\in -\frac12 +i\R$, corresponding to continuous representations of the algebra $\asl$.

In the $\Hp$ model all fields are either affine primaries or affine descendents thereof, and correlators of affine descendents can be deduced from correlators of affine primaries by the Ward identities. Therefore, in order to solve the model on the Riemann sphere with coordinates $z,\bz$, it is enough to determine the $n$-point functions of affine primaries for all $n$:
\bea
\Omega_n \equiv \la \prod_{i=1}^n \Phi^{j_i}(\mu_i|z_i) \ra\ .
\label{omn}
\eea
Now all such correlators of affine primaries are related to Liouville theory correlators as follows:
\bea
\Omega_n = \delta^{(2)}(\tsum_{i=1}^n\mu_i) |u|^2 |\Theta_n|^{\frac{1}{b^2}} \la \prod_{i=1}^n V_{\al_i}(z_i) \prod_{a=1}^{n-2} V_{-\frac{1}{2b}}(y_a)\ra\ ,
\label{htli}
\eea
where we consider Liouville theory at parameter
\bea
b = \frac{1}{\sqrt{k-2}} \ ,
\label{bk}
\eea
with primary operators $V_{\al}(z)$ with momenta
\bea
\al=b(j+1)+\frac{1}{2b}\ ,
\label{alj}
\eea
and conformal dimensions
\bea
\Delta_\al = \al(b+b^{-1}-\al)\ .
\label{dal}
\eea
The objects $u$ and $\Theta$ are defined by
\bea
u=\tsum_{i=1}^n \mu_iz_i \scs \Theta_n=\frac{\prod_{i<j} z_{ij} \prod_{a<b} y_{ab}}{\prod_{i=1}^n\prod_{a=1}^{n-2} (y_a-z_i)}\ ,
\label{uth}
\eea
while the positions $y_a$ of the operators $V_{-\frac{1}{2b}}(y_a)$ are determined in terms of $\mu_i,z_i$ by Sklyanin's change of variables
\bea
\sum_{i=1}^n \frac{\mu_i}{t-z_i} = u\frac{\prod_{a=1}^{n-2} (t-y_a)}{\prod_{i=1}^n (t-z_i)}\ .
\label{skl}
\eea

\subsection{Motivation of the ansatz}

Let us replace the fields $V_{-\frac{1}{2b}}$ in the $\Hp$-Liouville relation (\ref{htli}) with more general fields $V_{-\frac{m}{2b}}$ with $m\in \C$, and modify the prefactors as well:
\bea
\boxed{\Omega^{(m)}_n = \delta^{(2)}(\tsum_{i=1}^n\mu_i) |u|^{2\lambda} |\Theta_n|^{2\theta} \la \prod_{i=1}^n V_{\al_i}(z_i) \prod_{a=1}^{n-2} V_{-\frac{m}{2b}}(y_a)\ra}\ ,
\label{hmli}
\eea
where $\lambda$ and $\theta$ are numbers to be determined.
Can we still interpret $\Omega^{(m)}_n$ as an $n$-point function (\ref{omn}) of fields $\Phi^j(\mu|z)$ in some conformal field theory? In the process we keep the definitions of $u,\Theta$ and $y_a$ eqs. (\ref{uth},\ref{skl}), but the nature of the operator $\Phi^j(\mu|z)$ will be modified: it will now be a primary field with respect to an unknown symmetry algebra, with an unknown conformal dimension $\Delta^{(m)}_j$ with respect to a Virasoro algebra with an unknown central charge.

We hope that this interpretation of $\Omega^{(m)}_n$ exists for any choice of $m$, but we expect the values of the extra parameters $\lambda,\theta$ in (\ref{hmli}) to be determined in terms of $m$ by symmetry and other requirements.
Let us first consider the constraints on the three-point function due to global conformal invariance. This
requires that the dependence of $\Omega^{(m)}_3$ on the worldsheet coordinates $z_1,z_2,z_3$ should be
\bea
\Omega^{(m)}_3 \propto |z_{12}|^{-2\left(\Delta^{(m)}_{j_1}+\Delta^{(m)}_{j_2} -\Delta^{(m)}_{j_3}\right)} |z_{13}|^{-2\left(\Delta^{(m)}_{j_1}+\Delta^{(m)}_{j_3} -\Delta^{(m)}_{j_2}\right)}
|z_{23}|^{-2\left(\Delta^{(m)}_{j_2}+\Delta^{(m)}_{j_3} -\Delta^{(m)}_{j_1}\right)}
\ ,
\label{ommz}
\eea
with an arbitrary prefactor depending on $\mu_1,\mu_2,\mu_3$.
According to our ansatz, $\Omega^{(m)}_3$ is actually related to a four-point Liouville correlator, which behaves as
\begin{multline}
\la V_{\al_1}(z_1)V_{\al_2}(z_2)V_{\al_3}(z_3) V_{-\frac{m}{2b}}(y_1)\ra
\\ = |z_{12}|^{2\Delta_{-\frac{m}{2b}}-2\Delta_{12}} |z_{13}|^{-2\Delta_{-\frac{m}{2b}}-2\Delta_{13}} |z_{23}|^{2\Delta_{-\frac{m}{2b}}-2\Delta_{23}} |y_1-z_2|^{-4\Delta_{-\frac{m}{2b}}} {\cal G}(z)\ ,
\label{vvvv}
\end{multline}
where we use the notations $\Delta_{12}=\Delta_{\al_1}+\Delta_{\al_2}-\Delta_{\al_3}$ for the Liouville conformal dimensions, and ${\cal G}(z)$ for a known function of the cross-ratio $z=\frac{z_{32}(y-z_1)}{z_{31}(y-z_2)}$ whose precise form is not needed here. From the change of variables (\ref{skl}) we have $u(y-z_2) = \mu_2z_{12}z_{23}$ (in the limit $t\rar z_2$),
and in addition $z=1+\frac{\mu_3}{\mu_2}$ actually does not depend on $z_1,z_2,z_3$. Thus, the equations (\ref{hmli}) and (\ref{vvvv}) imply
\bea
\Omega^{(m)}_3 \propto |u|^{2\lambda+6\theta+4\Delta_{-\frac{m}{2b}}} |z_{12}|^{-2\theta-2\Delta_{-\frac{m}{2b}} -2\Delta_{12}} |z_{13}|^{-2\theta-2\Delta_{-\frac{m}{2b}} -2\Delta_{13}} |z_{23}|^{-2\theta-2\Delta_{-\frac{m}{2b}} -2\Delta_{23}}\ .
\eea
Comparing with the condition (\ref{ommz}) reveals that global conformal invariance requires
\bea
\lambda+3\theta+2\Delta_{-\frac{m}{2b}} = 0 \scs \Delta^{(m)}_{j_i} =\Delta_{\al_i}+\Delta_{-\frac{m}{2b}}+\theta\ .
\label{ltd}
\eea
In order to derive the extra relation which we need for fully determining $\lambda,\theta$ and $\Delta_{j_i}^{(m)}$, we will use a more heuristic reasoning. Consider the behaviour of our ansatz (\ref{hmli}) near $y_a=y_b$. In the $\Hp$ case ($m=1$), correlators are continuous at such points, a property which is particularly important in the study of the $\Hp$ model on the disc \cite{hr06}. More generally, in the cases when the Liouville field $V_{-\frac{m}{2b}}$ is degenerate, the leading behaviour of two such fields when coming close is
\bea
V_{-\frac{m}{2b}}(y_a) V_{-\frac{m}{2b}}(y_b) \underset{y_{ab}\rar 0}{\sim} |y_{ab}|^{-4\Delta_{-\frac{m}{2b}}+2\Delta_{-\frac{m}{b}}} V_{-\frac{m}{b}}(y_a)\ ,
\eea
and the behaviour of our ansatz is thus
\bea
\Omega_n^{(m)} \underset{y_{ab}\rar 0}{\sim} |y_{ab}|^{-4\Delta_{-\frac{m}{2b}}+2\Delta_{-\frac{m}{b}} +2\theta} \ .
\eea
Assuming the critical exponent $-4\Delta_{-\frac{m}{2b}}+2\Delta_{-\frac{m}{b}} +2\theta$ to vanish, and solving eq. (\ref{ltd}) as well, we obtain
\bea
\boxed{
\theta =\frac{m^2}{2b^2} \scs \lambda =m(1+b^{-2}(1-m)) \scs \Delta_{j}^{(m)}=\Delta_{\al} -\frac{m}{4}(2+2b^{-2}-b^{-2}m)}\ .
\label{tele}
\eea
These relations will be assumed to hold not only when the Liouville field $V_{-\frac{m}{2b}}$ is degenerate, but in all cases. Notice that it is possible to define a ``spin'' variable $j$ such that
\bea
\Delta^{(m)}_j=-(j+1)(b^2j+m-1) \ ,
\label{dmj}
\eea
in which case the momentum $\al$ of the corresponding Liouville field $V_\al(z)$ is
\bea
\al= b(j+1)+\frac{m}{2b} \ .
\label{aljm}
\eea

In the following we will argue that the ansatz (\ref{hmli}), together with the particular values (\ref{tele}) for the parameters $\lambda,\theta$ and the conformal weights of the fields $\Phi^j(\mu|z)$, has a meaning in terms of correlators in a conformal field theory.

\zeq\section{Symmetry algebra of the new theories}

We have checked that our ansatz is consistent with global conformal invariance, let us now study the rest of the conformal symmetry, and the possible extra symmetries which underlie our ansatz. To do this, it will be convenient to introduce a Lagrangian description of the corresponding theories. We will therefore propose such a description, check that it reproduces the relation (\ref{hmli}) with Liouville theory, and then use it for deriving the symmetries.

\subsection{Lagrangian description}

We use the same bosonic fields $(\phi,\beta,\g)$ as in the $\Hp$ model \cite{hos00}, and we propose the following Lagrangian and stress-energy tensor:
\bea
{\cal L}^{(m)} &=& \frac{1}{2\pi} \left[\p\phi\bp\phi +\beta\bp\g+\bar{\beta}\p\bg +b^2(-\beta\bar{\be})^m e^{2b\phi}\right]\ ,
\label{lm}
\\
T^{(m)} &=& -\be\p\g-(\p\phi)^2+(b+b^{-1}(1-m))\p^2\phi\ ,
\label{tm}
\eea
where $-\beta\bar{\beta}$ is assumed to be real positive.

The interaction term ${\cal L}^{(m)}_{int} = (-\beta\bar{\be})^m e^{2b\phi}$ is marginal with respect to the stress-energy tensor $T^{(m)}$. In the cases $m=0$ (Liouville theory) and $m=1$ ($\Hp$ model) it is known to be exactly marginal. This follows from the exponential dependence of the interaction term on $\phi$, a feature which is still present for arbitrary values of $m$. In perturbative calculations, many terms in the series expansion of $\exp -\int {\cal L}^{(m)}_{int}$ will then yield vanishing contributions due to $\phi$-momentum conservation in the free theory. We therefore expect the interaction to be exactly marginal, which
implies that the corresponding theories have conformal symmetry.

In the case $m=1$ of the $\Hp$ model, integrating out the non-dynamical fields $\beta,\bar{\be}$ in the path integral $\int {\cal D}\phi{\cal D}\beta{\cal D}\bar{\beta}{\cal D}\g{\cal D}\bg\  e^{-\int d^2w\ {\cal L}^{(m)}} $ yields a sigma model, whose target space is indeed $\Hp$. In the general case, it is still possible to integrate out $\beta,\bar{\be}$ if $\Re m>\frac12$, but the resulting Lagrangian has no sigma model interpretation because it involves higher powers of $\bp\g\p\bg$.

The relation between $\Hp$ and Liouville correlators has been rederived by Hikida and Schomerus using a path-integral computation \cite{hs07}. We will now emulate this calculation in order to rederive our ansatz (\ref{hmli}) from the path-integral definition of a theory with the Lagrangian (\ref{lm}). Of course, this path-integral definition will be complete only after we specify the fields $\Phi^j(\mu|z)$ in terms of $(\phi,\beta,\g)$:
\bea
\Phi^j(\mu|z)=|\mu|^{2m(j+1)} e^{\mu\g-\bar{\mu}\bg} e^{2b(j+1)\phi}\ .
\label{pjmz}
\eea
The path-integral definition of the $n$-point function is then
\bea
\Omega_n^{(m)} = \int {\cal D}\phi{\cal D}\beta{\cal D}\bar{\beta}{\cal D}\g{\cal D}\bg\ \ e^{-\int d^2w\ {\cal L}^{(m)}} \prod_{i=1}^n \Phi^{j_i}(\mu_i|z_i)\ .
\label{ommp}
\eea
Let us perform the integrations over $\g$ and $\bg$, and then $\beta$ and $\bar{\beta}$:
\bea
\Omega_n^{(m)} = \delta^{(2)}(\tsum_{i=1}^n\mu_i) \int {\cal D}\phi\  e^{-\frac{1}{2\pi}\int d^2w \left(\p\phi\bp \phi +b^2 \left|u\sum_{i} \frac{\mu_i}{w-z_i} \right|^{2m} e^{2b\phi} \right) } \prod_{i=1}^n |\mu_i|^{2m(j_i+1)} e^{2b(j_i+1)\phi}\ ,
\eea
where we still have $u=\sum_{i=1}^n \mu_iz_i$. We then perform the change of integration variable
\bea
\phi \rar \phi-mb^{-1}\log|u|\ .
\eea
This produces a global factor $|u|^{2m(1+b^{-2}(1-m))}$, due to an implicit worldsheet curvature term in the Lagrangian, which corresponds to the linear dilaton term $(b+b^{-1}(1-m))\p^2\phi$ in the stress-energy tensor $T^{(m)}$, eq. (\ref{tm}). (For simplicity we have used flat space as a model of the Riemann sphere and omitted the worldsheet curvature term. This subtlety is dealt with in \cite{hs07}.) Then, we define $y_a$ as the zeroes of $\sum_{i=1}^n\frac{\mu_i}{w-z_i}$ as in eq. (\ref{skl}), and perform the change of integration variable
\bea
\varphi(w)=\phi(w)+mb^{-1}\log\left|\frac{\prod_{a=1}^{n-2} (w-y_a)}{\prod_{i=1}^n (w-z_i)}\right|\ .
\eea
This yields
\begin{multline}
\Omega_n^{(m)} = \delta^{(2)}(\tsum_{i=1}^n\mu_i)\ |u|^{2m(1+b^{-2}(1-m))}\ |\Theta_n|^{\frac{m^2}{b^2}}
\\ \times
\int {\cal D}\varphi\ e^{-\frac{1}{2\pi}\int d^2w\left(\p\varphi\bp\varphi +b^2 e^{2b\varphi}\right)} \prod_{i=1}^n e^{(2b(j_i+1)+\frac{m}{b})\varphi(z_i)} \prod_{a=1}^{n-2} e^{-\frac{m}{b}\varphi(y_a)}\ ,
\end{multline}
where $\Theta_n$ was defined in eq. (\ref{uth}). The second line of this formula is the path-integral version of the Liouville theory correlator which appears in our ansatz (\ref{hmli}), with the expected values for the Liouville momenta $\al_i=b(j_i+1)+\frac{m}{2b}$. And the prefactors also agree with the expectations (\ref{tele}).

Therefore, the path-integral calculation provides a Lagrangian definition (\ref{lm}) for the new theories whose correlators we conjectured. This definition will allow us to easily study the symmetries of these theories.

\subsection{Symmetry algebra}

Let us interpret the theories with Lagrangian (\ref{lm}) as free theories of the fields $(\phi,\beta,\g,\bar{\beta},\bg)$ with contractions
\bea
\la \phi(z)\phi(w) \ra = -\log |z-w| \scs \la \beta(z)\g(w) \ra=\frac{1}{w-z}\ ,
\eea
deformed by the interaction term ${\cal L}^{(m)}_{int}=(-\beta\bar{\beta})^m e^{2b\phi}$. The chiral symmetry algebra is then the set of holomorphic fields whose OPEs with ${\cal L}^{(m)}_{int}$ vanish up to total derivatives. Such chiral fields can be constructed from the basic holomorphic fields $\p\phi,\beta,\g$ by using the normal-ordered product (\ref{abz}), see for instance \cite{bs92} for the rules of computing with this product.

We already know one chiral field, namely the stress-energy tensor $T^{(m)}$ (\ref{tm}), which generates a Virasoro algebra with central charge
\bea
c^{(m)} = 3+6(b+b^{-1}(1-m))^2\ .
\label{cm}
\eea
But in the case of the $\Hp$ model ($m=1$) we know that the creation modes of this Virasoro algebra are not enough for generating the full spectrum of the model from the fields $\Phi^j(\mu|z)$. These fields are indeed affine primaries, that is primary fields with respect to the much larger symmetry algebra $\asl$. Can we find a larger algebra for general values of $m$? Let us introduce the following holomorphic currents:
\bea
J^-&=&\beta\ ,
\label{jm}
\\
J^3&=&-\beta\g -mb^{-1}\p\phi\ ,
\label{jt}
\\
J^+&=&\beta\g^2+2mb^{-1}\g\p\phi-(m^2b^{-2}+2)\p\g\ ,
\label{jp}
\eea
where normal ordering is implicitly assumed when needed. The OPEs of these currents obey the relations
(\ref{jtjt}-\ref{jpjm}) of an $\asl$ algebra at level $k=2+m^2b^{-2}$. However, only the currents $J^-$ and $J^3$ are symmetries of our model. The current $J^+$ indeed has a nontrivial OPE with ${\cal L}^{(m)}_{int}$, and is no symmetry. And the stress-energy tensor which we could build from $J^-,J^3,J^+$ by the Sugawara construction (\ref{tjj}) is therefore also no symmetry. It actually differs from the
stress-energy tensor (\ref{tm}), with respect to which the interaction ${\cal L}^{(m)}_{int}$ is marginal. The chiral symmetry algebra is therefore generated by the three fields $T,J^3,J^-$ (where from now on we omit the superscipt of $T^{(m)}$), and we compute their OPEs as
\bea
T(z)T(w) &=& \frac{\frac12 c^{(m)}}{(z-w)^4} + \frac{2T(w)}{(z-w)^2} + \frac{\p T(w)}{z-w} + O(1)\ ,
\label{tt}
\\
T(z) J^-(w) &=& \frac{J^-(w)}{(z-w)^2} +\frac{\p J^-(w)}{z-w} +O(1)\ ,
\\
T(z) J^3(w) &=&\frac{(1-m)(1-mb^{-2})}{(z-w)^3}+
\frac{J^3(w)}{(z-w)^2} +\frac{\p J^3(w)}{z-w} +O(1)\ ,
\label{tjt}
\\
J^-(z)J^-(w)&=& O(1)\ ,
\\
J^3(z)J^-(w) &=& \frac{J^-(w)}{w-z}+O(1)\ ,
\\
J^3(z) J^3(w) &= &- \frac{1+\frac12 m^2b^{-2}}{(z-w)^2} +O(1)\ .
\label{jzjw}
\eea
This looks very much like the subalgebra of the affine algebra $\asl$ obtained by removing the current $J^+$, except that there is now a central term in the $TJ^3$ OPE, so that $J^3$ is no longer a primary field. Notice that this algebra, unlike the Lagrangian ${\cal L}^{(m)}$, is invariant under the duality
\bea
b\rar b^{-1}\scs m\rar mb^{-2}\ .
\eea
Notice also that setting $J^-=0$ yields a smaller algebra generated by $T$ and $J^3$, which might be interesting as well.\footnote{We could even consider a three-parameter family of $T,J^3$ algebras with arbitrary central terms $T(z)T(w) = \frac{\frac12 c}{(z-w)^4}+\cdots,\ T(z)J^3(w)=\frac{Q}{(z-w)^3}+\cdots $ and $ J^3(z)J^3(w)=-\frac{\frac{k}{2}}{(z-w)^2}+\cdots$. The relation $c=1-6\frac{Q^2}{k}$ defines a subfamily where the identification $T=-\frac{1}{k}(J^3J^3)+\frac{Q}{k}\p J^3$ is allowed. After introducing a boson $\varphi$ such that $J^3=\p\varphi$ this corresponds to a linear dilaton theory. Our parameters $m,b$ parametrize a different subfamily.}

It can be checked that the fields $\Phi^j(\mu|z)$ are primary with respect to our chiral algebra. We can indeed compute the OPEs of their free-field realization (\ref{pjmz}) with $J^-,J^3$ and $T$, which respectively reproduces the OPEs (\ref{jmph}), (\ref{jtph}) and (\ref{tph}) with however the conformal dimension $\Delta_j^{(m)}$ (\ref{dmj}). And we can check that the correlators (\ref{hmli}) have the correct behaviour under global symmetry transformations. We already performed this analysis in the case of the global conformal transformations of the three-point function $\Omega^{(m)}_3$, this is how we found $\Delta_j^{(m)}$ in the first place. The global Ward identity for $J^-$ is $(\sum_{i=1}^n \mu_i) \Omega_n^{(m)}=0$, which is obviously satisfied. We furthermore compute $\left(\sum_{i=1}^n \mu_i\pp{\mu_i} \right) \Omega_n^{(m)} = -(1-m)(1-mb^{-2}) \Omega_n^{(m)}$. This is what is expected knowing that $J^3$ is no longer primary, see the $TJ^3$ OPE (\ref{tjt}).

These simple consistency checks leave two questions about our determination of the symmetry algebra:
\begin{enumerate}
 \item {\bf Is the symmetry algebra large enough?} We still have to show that the descendent fields obtained by repeatedly acting on the primaries $\Phi^j(\mu|z)$ with the creation modes of $T,J^3,J^-$ do span the spectrum. In particular, can the $\Phi^{j_1}(\mu_1|z_1)\Phi^{j_2}(\mu_2|z_2)$ OPE be written as a sum over such descendents? In principle, we could address this issue by studying the $z_{12}\rar 0$ expansion of our ansatz (\ref{hmli}) for the correlators $\Omega_n^{(m)}$. This would however be tedious. Instead, let us focus on the $m=1$ case. The spectrum of the $\Hp$ model is known to be generated by the modes of $J^3,J^+,J^-$, but we will now argue that the modes of $T,J^3,J^-$ are actually enough. Let us define these modes by $T(z)=\sum_{n\in\Z} L_n z^{-n-2}$ and $J^a(z)=\sum_{n\in\Z} J^a_n z^{-n-1}$; creation modes are $J^a_{n<0}$ and $L_{n<0}$, while primary fields $\Phi^j(\mu|z)$ correspond to primary states $|p\rangle$ such that $L_{n>0}|p\rangle = J^a_{n>0}|p\rangle=0$.
 Any level one $J^+$-descendent state can by definition be written as $|d\rangle= J^+_{-1}|p'\rangle$ with $|p'\rangle$ an affine primary state in the $\Hp$ spectrum. The spectrum being made of continuous representations, this primary can be rewritten as $|p'\rangle = J_0^-|p\rangle$ with $|p\rangle$ another primary. Using the Sugawara construction (\ref{tjj}), we then have
 \bea
 |d\rangle =  J^+_{-1}J_0^-|p\rangle =\left[-J^-_{-1}J^+_0 +2J^3_{-1}J^3_0 +(k-2)L_{-1}\right] |p\rangle\ ,
 \label{dp}
 \eea
 which is manifestly a combination of $L_{-1},J^3_{-1},J^-_{-1}$-descendents of affine primary states. This reasoning can be iterated to higher level $J^+$-descendent states. This proof is special to $m=1$ and cannot be generalized, but it demonstrates that our $T,J^3,J^-$ symmetry algebra is likely large enough.

 \item {\bf Are the chiral fields algebraically independent?} In the $\Hp$ model, the fact that the chiral fields $T,J^+,J^3,J^-$ are not independent but related by the Sugawara construction implies that the correlators obey Knizhnik--Zamolodchikov differential equations. In our generalized theories with parameter $m$, correlators (\ref{hmli}) do obey differential equations for values of $m$ such that the field $V_{-\frac{m}{2b}}$ is a Liouville degenerate field. This happens if
 \bea
 m = p + b^2 q \scs p,q=0,1,2\cdots
 \label{mpq}
 \eea
 We therefore expect that the structure of our chiral algebra becomes in some sense reducible for these values of $m$, so that differential equations can be derived for the correlators. This is what we will  explicitly demonstrate in the case $m=2$.
\end{enumerate}

\zeq\section{Differential equation in the case $m=2$}

We will first derive the third-order differential equations satisfied by the correlator $\Omega^{(2)}_n$ from the Belavin--Polyakov--Zamolodchikov equations satisfied by the corresponding Liouville correlators, and then check that these equations can be recovered from our symmetry algebra.

\subsection{Third-order BPZ equation}

The Virasoro module generated by the Liouville field $V_{-\frac{1}{b}}$ has a null vector at level three \cite{bpz84}:
\bea
\chi_3 = \left[(-1+2b^{-2}) L_{-3} +2L_{-1}L_{-2}+\frac12 b^2 L_{-1}^3\right] V_{-\frac{1}{b}}\ .
\label{chit}
\eea
Assuming that this null vector vanishes implies that correlators involving $V_{-\frac{1}{b}}$ obey third-order BPZ differential equations. In particular, let us write the BPZ equation associated to a degenerate field $V_{-\frac{1}{b}}(y)$ in the Liouville correlator which appears in our ansatz (\ref{hmli}). We call $y_b\neq y$ the insertion points of the other degenerate fields so that $y_a=(y,y_b)$; moreover we call $z_I=(z_i,y_b)$ the positions of all fields except  $V_{-\frac{1}{b}}(y)$. The BPZ equation then involves the following differential operator:
\bea
{\cal D} = \frac{b^2}{2} \frac{\p^3}{\p y^3}
+ \sum_I\left[\pp{y}  \frac{2}{y-z_I}\pp{z_I} + \frac{2\Delta_{\al_I}}{(y-z_I)^2}\pp{y} \right]
+ \sum_I \left[\frac{\Delta_{-\frac{1}{b}}+2}{(y-z_I)^2}\pp{z_I}+ \frac{2\Delta_{-\frac{1}{b}}\Delta_{\al_I}}{(y-z_I)^3}\right]  \ .
\eea
This BPZ equation implies ${\cal D}' \Omega_n^{(2)}= 0$ where ${\cal D}'=\Theta_n^\frac{2}{b^2} {\cal D} \Theta_n^{-\frac{2}{b^2}}$, with $\Theta_n$ defined by eq. (\ref{uth}). We thus wish to compute ${\cal D}'$; at the same time we should perform the change of variables $(z_i,y_a)\rar (z_i,\mu_i)$ defined by eq. (\ref{skl}). In particular we should rewrite $\pp{z_i}=\left.\pp{z_i}\right|_{y_a} $ in terms of $\frac{\delta}{\delta z_i} \equiv \left.\pp{z_i}\right|_{\mu_j}$. This will be done thanks to the identity \cite{rt05}
\bea
\sum_{i=1}^n\frac{1}{y-z_i}\pp{z_i} +\sum_b \frac{1}{y-y_b} \pp{y_b} -X\pp{y} = \sum_{i=1}^n \frac{1}{y-z_i}\frac{\delta}{\delta z_i}\ ,
\label{dzeq}
\eea
where we defined
\bea
X \equiv \sum_b\frac{1}{y-y_b}-\sum_{i=1}^n \frac{1}{y-z_i} = -\frac{\sum_{i=1}^n \frac{\mu_i}{(y-z_i)^3}}{\sum_{i=1}^n \frac{\mu_i}{(y-z_i)^2}} \ .
\label{xdef}
\eea
We also use
\bea
\pp{y} = \sum_{i=1}^n \frac{\mu_i}{y-z_i} \pp{\mu_i}\ .
\label{ppy}
\eea
Explicit calculations yield
\begin{multline}
{\cal D}'= \frac{b^2}{2} \frac{\p^3}{\p y^3} -X\ppd{y} +2 \pp{y} L_{-2}(y) -4b^{-2} X L_{-2}(y)
\\
+(2b^{-2}-1)\left[L_{-3}(y)-\sum_i \frac{\mu_i}{(y-z_i)^3}\pp{\mu_i} -X \sum_i\frac{\mu_i}{(y-z_i)^2}\pp{\mu_i}\right]\ ,
\label{tdt}
\end{multline}
where we defined
\bea
L_{-2}(y) &=& \sum_i\frac{1}{y-z_i}\left(\frac{\delta}{\delta z_i} +\frac{\Delta_{j_i}^{(2)}}{y-z_i}\right)\ ,
\label{lmdy}
\\
L_{-3}(y)&=&-\sum_i\frac{1}{(y-z_i)^2}\left(\frac{\delta}{\delta z_i} +\frac{2\Delta_{j_i}^{(2)}}{y-z_i}\right) \ ,
\label{lmty}
\eea
where the conformal dimensions $\Delta_{j_i}^{(2)}$ and $\Delta_{\al_i}$ are related by eq. (\ref{tele}).

The operator ${\cal D}'$ can be understood as a generalization of the $s\ell_2$ Knizhnik--Zamolodchikov differential operator, which in our notations can be written as \cite{rt05}
\bea
{\cal D}^{KZ} = b^2 \ppd{y} + L_{-2}(y)\ .
\eea

\subsection{Reformulation of the BPZ equation in terms of symmetry generators}

If our identification of the symmetry algebra is correct, the differential equation ${\cal D}'\Omega^{(2)}_n=0$ should have a reformulation in terms of the chiral fields $T,J^3,J^-$. This is a non-trivial requirement on ${\cal D}'$, and we will now show that it is satisfied.

Let us denote $\la {\cal Q}\ra =\la \prod \Phi^{j_i}(\mu_i|z_i)\ra$. The actions of differential operators $\pp{y} $, $L_{-2}(y)$ and $L_{-3}(y)$ on $\la {\cal Q}\ra$ have immediate interpretations as insertions of the chiral fields $J^3(y),T(y)$ and $\p T(y)$, for instance
\bea
\pp{y} \la {\cal Q}\ra = \la \sum_i\oint_{z_i}dt \frac{J^3(t)}{y-t} {\cal Q} \ra = \la \oint_y dt\frac{J^3(t)}{t-y} {\cal Q} \ra = \la J^3(y) {\cal Q}\ra \ ,
\eea
where we used the formula (\ref{ppy}) for $\pp{y} $ and the OPE (\ref{jtph}) of $J^3$ with $\Phi^j(\mu|z)$. Iterating the actions of such differential operators yields results like
\bea
 \pp{y} L_{-2}(y) \la {\cal Q}\ra = \pp{y}\la T(y) {\cal Q} \ra = \la \p T {\cal Q}\ra +\la (J^3T)(y) {\cal Q}\ra
\ ,
\eea
where the normal-ordered product $(J^3T)$ is defined as previously, see eq. (\ref{abz}). Moreover, we have
\bea
\sum_i\frac{\mu_i}{(y-z_i)^3} \pp{\mu_i} \la {\cal Q}\ra = \frac12 \la \sum_i \oint_{z_i}dt \frac{\p^2J^3(t)}{y-t} {\cal Q}\ra = \la \tfrac12\p^2J^3(y){\cal Q}\ra\ .
\eea
Finally, the factors of $X$ in ${\cal D}'$ can be related to insertions of $\p J^- $ and $\p^2 J^-$, thanks to eq. (\ref{xdef}) and identities of the type
\bea
\sum_i\frac{\mu_i}{(y-z_i)^3} \la {\cal P}(y) {\cal Q}\ra = \frac12 \la \oint_y dt\frac{\p^2J^-(t)}{t-y} {\cal P}(y) {\cal Q}\ra = \la \tfrac12 (\p^2J^- {\cal P})(y)\ {\cal Q} \ra\ ,
\eea
which is valid for any operator ${\cal P}$.

Therefore, the equation ${\cal D}'\Omega_n^{(2)}=0$ with the operator ${\cal D}'$ given in eq. (\ref{tdt}) can be rewritten as $\la {\cal R}(y) \prod \Phi^{j_i}(\mu_i|z_i)\ra=0$, where
\begin{multline}
{\cal R}=\tfrac12 b^2 (\p J^-(J^3(J^3J^3)))+2 (\p J^-( J^3T))+[2b^{-2}+1] (\p J^-\p T)
\\
+\tfrac32 b^2 (\p J^-(J^3\p J^3))+ \tfrac12 [b^2+1-2b^{-2}] (\p J^- \p^2J^3)
\\
-\tfrac12 (\p^2 J^-(J^3J^3))+[-1+b^{-2}](\p^2 J^-\p J^3)-2b^{-2}(\p^2J^-T)\ .
\label{rop}
\end{multline}
We can already conjecture that, for all the values (\ref{mpq}) of $m$ such that the fields $V_{-\frac{m}{2b}}$ is degenerate, the BPZ equations can similarly be rewritten in terms of operators $T,J^-,J^3$. It is however not clear how to deduce our operator ${\cal R}$ from a null vector like (\ref{chit}), without performing the explicit calculations as we did.

The equation $\la {\cal R}(y) \prod \Phi^{j_i}(\mu_i|z_i)\ra=0$ of course does not mean that the operator ${\cal R}$ should be set to zero, because this equation is valid only at special points $y=y_1\cdots y_{n-2}$. These points were defined (\ref{skl}) as the zeroes of $\varphi(t)=\sum_{i=1}^n\frac{\mu_i}{t-z_i}$; they can be characterized in terms of the operator $J^-$ by
\bea
\la J^-(y) \prod_{i=1}^n \Phi^{j_i}(\mu_i|z_i) \ra = 0\ .
\eea
Actually, for any operator ${\cal P}$ we have $\la (J^-{\cal P})(y) \prod_{i=1}^n \Phi^{j_i}(\mu_i|z_i) \ra = 0$. Therefore, the operator ${\cal R}$ is expected to vanish modulo operators of the type $(J^-{\cal P})$.

In other words, we expect that this operator corresponds to a subsingular vector ${\cal R}|0\rangle$ in the vacuum module of our symmetry algebra. That is, if we would set the singular vector $J^-|0\rangle$ to zero, then ${\cal R}|0\rangle$ would become a singular vector in the resulting coset module. We are actually not setting $J^-|0\rangle$ to zero, but the presumptive subsingular vector ${\cal R}|0\rangle$ is nevertheless associated to differential equations satisfied by the correlation functions. Relations between subsingular vectors and differential equations were found previously by Dobrev \cite{dob95} in the context of finite-dimensional symmetry algebras, but they do not seem widespread in conformal field theory so far.
\footnote{I am very grateful to Vladimir Dobrev for pointing out that the notion of a subsingular vector is relevant here, and for patiently explaning some of the literature on this topic to me.}

\subsection{Subsingular vectors of the symmetry algebra}

In order to show that the third-order differential equation can be deduced from our symmetry algebra, we still have to prove that the operator ${\cal R}$ (\ref{rop}) corresponds to a subsingular vector. We will actually investigate the more general operator
\begin{multline}
{\cal R}_{\{\lambda_i\} } = \lambda_1 (\p J^-J^3J^3J^3) + \lambda_2(\p J^-J^3T) + \lambda_3(\p J^-\p T) + \lambda_4 (\p J^-J^3\p J^3) + \lambda_5(\p J^-\p^2J^3)
 \\
  + \lambda_6 (\p^2J^-J^3J^3)+ \lambda_7 (\p^2J^- \p J^3) + \lambda_8(\p^2J^-T)\ ,
\label{rli}
\end{multline}
which depends on arbitrary coefficients $\lambda_1\cdots \lambda_8$.
Here and in the following we use the shorthand notation $ABCD=(ABCD)=(A(B(CD)))$ for multiple normal orderings, see \cite{bs92} for more details on calculations involving such expressions.

We will perform this investigation with the help of the free fields $(\phi,\beta,\g)$. Since the map from $(J^-,J^3,T)$ to $(\phi,\beta,\g)$ defined by the equations (\ref{jm}), (\ref{jt}) and (\ref{tm}) is a morphism of algebras, it can indeed be used for determining whether ${\cal R}_{\{\lambda_i\} }$ generates a nontrivial ideal of the coset algebra obtained by modding out the ideal generated by $J^-$. (This is the algebraic formulation of our subsingular vector problem.)
So let us compute the operator ${\cal R}_{\{\lambda_i\} }$ in terms of the fields $(\phi,\beta,\g)$, modulo operators of the type $(J^-{\cal P})=(\beta {\cal P})$. We will denote by $\simeq$ the equality of operators modulo such terms. For example, we find
\bea
(J^3(J^3J^3))&\simeq& 2\p\be\p\g-\tfrac12\p^2\be\g-3mb^{-1}\p\be\g\p\phi-m^3b^{-3}\p\phi^3\ ,
\\
(J^3T)&\simeq& \p\be\p\g+mb^{-1}\p\phi^3-m(1+b^{-2}(1-m))\p\phi\p^2\phi\ ,
\\
(J^3\p J^3)&\simeq& \tfrac12\p^2\be\g+mb^{-1}\p\be\g\p\phi+m^2b^{-2}\p\phi\p^2\phi\ ,
\\
(\p T) &\simeq& -\p\be\p\g-2\p\phi\p^2\phi+(b+b^{-1}(1-m))\p^3\phi\ ,
\\
(\p^2J^3)&\simeq & -\p^2\be\g-2\p\be\p\g-mb^{-1}\p^3\phi\ .
\eea
We then compute
\begin{multline}
{\cal R}_{\{\lambda_i\} }\simeq\left[2\lambda_1+\lambda_2-\lambda_3-2\lambda_5\right] \p\beta^2\p\g +\left[-3mb^{-1}\lambda_1+mb^{-1}\lambda_4\right] \p\be^2\g\p\phi
\\
+\left[-m^3b^{-3}\lambda_1+mb^{-1}\lambda_2\right] \p\be\p\phi^3
+\left[-m(1+b^{-2}(1-m))\lambda_2-2\lambda_3+m^2b^{-2}\lambda_4\right] \p\be\p\phi\p^2\phi
\\
+\left[(b+b^{-1}(1-m))\lambda_3-mb^{-1}\lambda_5\right]\p\be\p^3\phi
+\left[-\tfrac12\lambda_1+\tfrac12\lambda_4-\lambda_5+\lambda_6-\lambda_7\right]\p\be\p^2\be\g
\\
+\left[m^2b^{-2}\lambda_6-\lambda_8\right]\p^2\be\p\phi^2
+\left[-mb^{-1}\lambda_7+(b+b^{-1}(1-m))\lambda_8\right]\p^2\be\p^2\phi\ .
\end{multline}
Let us solve the equation ${\cal R}_{\{\lambda_i\} }\simeq 0$, which when satisfied implies that ${\cal R}_{\{\lambda_i\} }$ corresponds to a subsingular vector. This equation leads to a system of 8 linear equations for the 8 unknowns $\lambda_1\cdots \lambda_8$. Actually, the first five equations form a closed subsystem of equations for $\lambda_1\cdots \lambda_5$. This subsystem has a nonzero solution only if its determinant vanishes, that is if
\bea
(m-1)(m-2)(m-b^2)(m-2b^2)=0\ .
\eea
The four solutions of this equation correspond to the Liouville operators $V_{-\frac{m}{2b}}$ being degenerate, leading to BPZ differential equations of order 2 or 3. This is therefore a strong check of our claim that the ansatz (\ref{hmli}) does define conformal field theories with symmetry algebras generated by $T,J^3,J^-$. Let us perform a more detailed check in the case $m=2$, by explicitly computing the nonzero solution to the system ${\cal R}_{\{\lambda_i\} }=0$:
\bea
\begin{array}{c}
\lambda_1=\tfrac12 b^2\scs \lambda_2=2\scs \lambda_3=2b^{-2}+1 \scs \lambda_4=\tfrac32 b^2 \scs \lambda_5 = \tfrac12(b^2+1-2b^{-2}) \ ,
\vspace{2mm}
\\
\lambda_6=-\tfrac12 \scs \lambda_7=-1+b^{-2} \scs \lambda_8=-2b^{-2}\ .
\end{array}
\eea
With these values of of $\lambda_i$, the operator ${\cal R}_{\{\lambda_i\} }$ (\ref{rli}) does agree with the operator ${\cal R}$ (\ref{rop}), which we found by reformulating the third-order BPZ equation.

\zeq\section{Concluding remarks}

We have argued that for any choice of $m$ and the central charge $c$, the object $\Omega_n^{(m)}$ of eq. (\ref{hmli}) can be interpreted as an $n$-point correlation function in a conformal field theory with a chiral symmetry algebra generated by the fields $T,J^3,J^-$ with OPEs (\ref{tt}-\ref{jzjw}). This conformal field theory is solvable in the sense that its correlation functions are known in terms of Liouville correlation functions. Liouville theory itself has been solved in the sense that its three-point function on the sphere is explicitly known, while its $n$-point functions on arbitrary Riemann surfaces can in principle be deduced thanks to the conformal symmetry of the theory. (See \cite{tes01a} for a review.) The solution of the new theory is therefore not very explicit, and no closed formula can be written for its three-point function except for some ``degenerate'' values of $m$ (\ref{mpq}) when it satisfies a differential equation.

This differential equation provided the most non-trivial test of our claims. In the case $m=2$, we compared the differential equation deduced from our chiral symmetry algebra with the third-order BPZ equation, and found explicit agreement. We expect such an agreement to hold for all degenerate values of $m$, and it would be interesting to check this beyond case-by-case calculations.

There may exist other theories based on the same symmetry algebra. For instance, in the case $m=1$, the non-rational, non-unitary $\Hp$ model shares its symmetry algebra with the unitary $AdS_3$ WZW model and with the rational $SU_2$ WZW models.
For general values of $m$, our model remains non-rational and non-unitary. (The lack of unitarity still follows from Gawedzki's $\Hp$-model argument \cite{gaw91}, although it is not quite clear what the scalar product on the spectrum is, as $J^-$ has no conjugate field.) It would be interesting to construct rational or unitary theories based on the same symmetry algebra. Note however that our reasoning around eq. (\ref{dp}), which showed that in the case $m=1$ the modes of $T,J^-$ and $J^3$ did generate the whole $\Hp$ spectrum, relied on the fact that the spectrum is purely continuous. But the $AdS_3$ and $SU_2$ WZW models involve discrete and finite-dimensional representations respectively, which presumably cannot be generated from the modes of $T,J^-$ and $J^3$. Therefore, a rational theory based on the $(T,J^3,J^-)$ algebra would probably differ from the $SU_2$ WZW model and have a smaller spectrum.

We have not assumed any restrictions on the choice of the parametrs $m$ and $c$. For some purposes it might be useful to restrict say the central charge of the theory and the conformal dimensions of the fields to be real. Such restrictions could be dictated by particular applications.
From the point of view of conformal field theory, the new theories are however well-defined, and their correlators manifestly satisfy crossing symmetry, a very stringent constraint. It is therefore possible to study issues like the solution of these theories on Riemann surfaces with boundaries.

\acknowledgments{I am grateful to Volker Schomerus, Thomas Quella and Vladimir Fateev for useful discussions and comments on the manuscript, and to DESY, Hamburg for hospitality while part of this work was done. In addition, I thank the theoretical physics groups at King's College London and Sogang University in Seoul for listening and reacting to informal talks on this subject.}

\input{refs.tex}

\end{document}

redpajama_set_name: RedPajamaArXiv


Welcome to Electric Bikes Sussex.
We stock a large range of leading Electric Bike brands and have more than 10 different Motor systems for you to choose from!
Our entire focus is your satisfaction, so let us help you on your journey.


BT has made a commitment to upgrade every customer in the UK to our all IP voice service by 2025. This will give customers a better experience with features like HD calling, and crucially will lay the foundations for converged communications where we will be able to offer IP services to customers across calls, Broadband and Mobile – a unique opportunity for BT as a company with the UK's best Broadband, Wi-Fi and Mobile coverage. The digital team is working with teams across BT to launch this product to customers next year, alongside the delivery of a value proposition that will promote the benefits of taking all of BT products and ensure existing customers get the best value.
The key purpose of this role is to own the digital experience for the digital voice product after the point of acquisition. We have developed some capability already, including the ability to manage calling features, which will need to be launched and optimized in parallel to working on the next phase of the produce. Working with key stakeholders across commercial, process, operation, product-line, marketing, online and engineering teams; the role holder will act as the online expert responsible for the creation and definition of the detailed UX requirements. They will be responsible for overseeing the creation of all UX wireframes and interactive Axure prototypes in collaboration with our in-house studio. They will be responsible for ensuring that all digital components of the work are delivered effectively, on time and in a way that provides the best customer experience and optimum realisation of benefits.
1. Experience of building digital experiences - The job holder will be responsible for the digital experience for digital voice. They will understand what it takes to deliver a world class digital experience for a new product and will be able to apply this experience directly to ensure the product delights BT's customers.
2. Digital requirements analysis and detailed definition. The job holder will work with key stakeholders in the existing customer and customer care teams to understand the high level objectives and requirements they have to deliver an improved service experience to customers online. The job holder will decompose these high level requirements into detailed, low level requirements for digital development and implementation. These requirements are well-formed, testable, provide appropriate detail and coverage for online / digital implementation and ensure outcomes which are consistent with the commercial, brand and experience targets and objectives of BT Consumer.
3. Wireframes and prototype development using Axure. The job holder will be responsible for managing the creation of all required user experience assets to support the digital implementation process. It is your idea that you are bringing to life. While you sketch it out, typically our studio resources produce the actual wireframes and prototypes for you. However, you should have experience producing wireframes yourself, preferably in Axure. Your wireframes and prototypes will be used as the tool to tease out requirements, and walk technical architects through them to determine feasibility. You will have support from studio resources to do the bulk of the wireframe / prototyping process, however we expect you to be able to do this yourself so that you are able to review the quality of work being provided by the studio.
4. Customer Acceptance Testing & Verification. The job holder will be responsible for ensuring that testing of the digital implementation fully covers the customer journeys, and that any issues are appropriately prioritised for fix in the context of the overall project delivery.
5. Digital Trial & Launch. The job holder will be responsible for supporting the trial and launch phases of major digital capability.
So why join the digital content team at BT Sport? We act like a start-up in a major FTSE 100 business, able to make decisions that drive big changes to how our customers interact with BT.
Our aim is to create compelling digital content that engages and helps customers, and we are building a team of digital editorial experts at the heart of our TV operation in Stratford.


It's very vital that a leader maintains consistency in his methods as well as expectations for his employees. A great leader knows the leadership theories and styles and avoids sending missed signals and is confident about proven ways of doing things. Such a leader does not change attitude, organizational values, or business principles with the flow of the tide.
A great leader must be assertive all the time. That does not mean that he's stubborn, rather, it implies that he's willing to take bold measures without wavering to achieve desired results.
Any successful leader is humble enough to treat his juniors with respect and admit his mistakes. Humility means that the leader who has good leadership qualities must be willing to learn from past experiences, peers, and even juniors in order to advance strategic interests.
A great leader does not preach water and drink wine. He leads by example in all aspects of corporate governance. If he expects employees to report to work in time, he knows that there can be no exemptions, including himself. In matters of professional and financial integrity, the leader must maintain a clean record.
A hands-on leadership is an admired style, although leaders who learn to delegate can also be successful. The greatest of all leaders must learn to tell when its right to lead from the front line and when it's more effective to delegate. A leader that's not hands-on is less involved and he may not fully understand what needs to be done on the ground to get things done. On the other hand, a leader that does not delegate responsibilities is unable to mentor and also runs the risk of compromising the integrity and proficiency of business operations when he's not available.
Of course, a great leader must work hard to take his organization to greater heights. However, the trend nowadays is to work smart. Working smart involves innovation and creative thinking to come up with more cost-effective ways of doing things. It entails the reduction of physical strain and effort to get the job done when there are more efficient ways to achieve good results.
In the contemporary world, having some leadership attributes can give a person an added advantage in life. Indeed, there is an acute shortage of people with leadership qualities in various organizations today. There are many people who still harbor the false belief that leaders are born. In actual sense, anyone can become a leader with the right training. There are various programs today that have been devised for training leaders. Accordingly, choosing a suitable program can be quite of a tall order.
There are various organizations today that have elected to train their own leaders. Such leaders who have people management skills are usually trained to take up various responsibilities at such organizations. For instance, there is a high demand for supervisors in various organizations. There are also various organizations that train their employees to take up managerial positions at the organizations. When an organization has a good management, the profitability will increase by leaps and bounds. There are also many organizations that train their employees to take up the job of an executive. When a person aspires to become a leader, the first step is to understand the attributes that make a person a leader.
You can base this from the leadership skills list. A good leader should always have the zeal required to implement the projects that are pending. Honesty is very important for any person that aspires to become a leader. Without ethical standards, it is highly unlikely that a person will climb the ladder to become a leader in the future. When a leader is honest, the other employees will follow suit and observe those standards. This will enable the company to create a good picture in the eyes of prospective clients and hence increase their growth.
For any leader to become successful, he must nurture ethical standards that should be observed at all the times. For a person to become a leader, it is important to learn about how to delegate. The leader should only focus on the bigger picture at the organization. This will enable the business to attain higher goals that have been set. Indeed, it is very hard to create a successful organization before learning the art of delegation. If the leader does not learn how to delegate, the work might end up piling up and hence disappoint the clients. This might make it harder for the business to remain competitive in the industry since it is unable to meet the expectations of their loyal clients.


I like to make this French Vanilla Smoothie as a special treat every once in a while. It DOES contain calories and caffeine. So please, be careful not to make it too often.
A great thing about this smoothie recipe is that it doesn't require a high powdered blender as some of the other recipes.
Blend the instant powder with the water and ice. It made 4 cups of smoothie. Three of us drank the smoothie. Enjoy!!!
This recipe is not as healthy as using dates or stevia, because it uses evaporated cane sugar. But this can be a healthier alternative to a coffee smoothie from Star Bucks.


text:
The 1999 Direct Line International Championships was a tennis tournament played on grass courts at the Eastbourne Tennis Centre in Eastbourne in the United Kingdom that was part of Tier II of the 1999 WTA Tour. The tournament was held from 14 June until 19 June 1999. Natasha Zvereva won the singles title.

Entrants

Seeds

Other entrants
The following players received wildcards into the singles main draw:
  Samantha Smith
  Karen Cross
The following players received wildcards into the doubles main draw:
  Julie Pullin /  Lorna Woodroffe

The following players received entry from the singles qualifying draw:

  Louise Latimer
  Elena Tatarkova
  Mariaan de Swardt
  Anne-Gaëlle Sidot

The following players received entry from the doubles qualifying draw:

  Maja Murić /  Christína Papadáki

Finals

Singles

 Natasha Zvereva defeated  Nathalie Tauziat, 0–6, 7–5, 6–3
 It was Zvereva's only singles title of the year and the fourth of her career.

Doubles

 Martina Hingis /  Anna Kournikova defeated  Jana Novotná /  Natasha Zvereva, 6–4 retired

References

External links
 ITF tournament edition details

Direct Line International Championships
Eastbourne International
1999 in English women's sport
June 1999 sports events in the United Kingdom
1999 in English tennis

redpajama_set_name: RedPajamaWikipedia


text:
Digital Transformation » Big Data » How does a finance team build a strategy around AI?
How does a finance team build a strategy around AI?
Richard Sampson, SVP EMEA, insightsoftware shares a strategic view for Financial Teams towards implementing Artificial Intelligence (AI).
by Richard Sampson | insightsoftware - November 1, 2019
As Artificial Intelligence (AI) gains momentum and becomes more sophisticated, it will change the financial world and how finance teams work.
AI is a broad term, so understanding how it slots into financial technology and the role of automation is important when planning an AI strategy that is fit for the future.
Through machine learning and neural networks, AI has the ability to recognise patterns in complex data sets far quicker and with far greater accuracy than a human can manage. When this capability is harnessed with other complementary technologies, AI has the potential to transform business processes, introducing huge efficiencies.
AI is much further off than people think in terms of full-blown adoption. The transition will be gradual, as AI is only part of the story. That means strategically planning your adoption of AI as the technology matures.
Today, AI isn't even top of finance's new technology wish list. According to a survey cited in Gartner's Magic Quadrant for Cloud Financial Planning and Analysis Solutions, forty-six percent of respondents said predictive analytics is where they intended to invest the most money before 2021. The second ranked technology was robotic process automation (43%), followed by artificial intelligence/machine learning (35%).
Financial sector leading the UK in use of AI
A new report from Microsoft has found that the Financial Sector is leading the UK in the use of AI technology, but the industry is at a tipping point, and to fully benefit from such technologies, organisations need to invest now.
AI for Financial Directors and CFOs
CFOs and Financial Directors are using AI to enhance the accuracy of trading, drive better decision making, spot fraud earlier and boost compliance.
This is rather telling, because it indicates a specific plan of action which starts with data analytics and automation, followed by process automation, and finally AI.
So how do you plan for the future?
First things, first. You line up and enhance existing software focusing on the low-hanging fruit: data automation.
To plan for the future with AI in mind, a finance team needs to review any clunky, manual, and error-prone processes that are in need of a refresh to ensure data automation and data quality is made a priority.
Anyone working in finance knows that manually dumping data into Excel and manipulating it is error-prone, not to mention unbelievably time-intensive. In recent years, this process has been fully automated with financial reporting software, making real-time data access possible throughout the month. Accountants can drill from summary data into balances, journals, or subledgers to investigate variances and fix reconciliation issues.
The productivity gains are huge, and we're seeing the majority of finance teams reporting in this way, no matter the organisation size or ERP system.
Once data automation and analysis is the "new norm" for a company, finance teams should start thinking about process automation in the guise of robotic process automation (RPA).
According to the IEEE Standards Association (IEEE SA), RPA refers to the use of a "preconfigured software instance that uses business rules and predefined activity choreography to complete the autonomous execution of a combination of processes, activities, transactions, and tasks in one or more unrelated software systems to deliver a result or service with human exception management."
This looks like a long-winded explanation, but it very much reflects what's starting to happen within finance teams.
RPA is very effective. Studies indicate it can reduce repetitive data entry tasks by 80 percent in accounts payable, financial close, and tax accounting. RPA is able to read data from one source and then automatically enter it into an ERP system. A financial or operational report is only as good as the data inside the ERP system. RPA can help quickly ensure that data is both accurate and exactly where it needs to be, leading to further productivity gains.
However, don't mistake this type of tech for AI. RPA is only mimicking human behaviour, not "thinking" like a human. Nevertheless, RPA is a conduit to enabling AI in the future, so we strongly recommend that finance teams build RPA into their future technology plans.
AI takes centre stage
RPA sets the stage to something called "intelligent automation." Intelligent automation is a combination of process-driven tasks (RPA) and data-driven tasks (AI).
AI understands the meaning of data, whereas RPA focuses purely on a process. Take invoices: That process is programmed to understand a specific way of working in strict parameters. If you introduce a new supplier, invoice template, different tax rates, or any new data point, RPA is flummoxed. You need AI to make sense of this new information and how to handle it by "thinking" for itself.
Once the initial steps of automation (data and process) are managed internally, you've set the stage for AI to shine. The applications of AI in finance are already numerous, and it shows particular promise as a supporting technology for risk management and compliance.
While finance has proven to be an early adopter of AI in comparison to other industries, AI as mainstream is still a while away. An increased demand for understanding data patterns has directly contributed to the growth in demand for AI, and the future of finance is going to be heavily influenced by AI's ability to set the stage for increasing competitiveness.
Richard Sampson is the SVP EMEA at financial reporting specialist, insightsoftware.
AI for Finance
Future of Finance


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Abstract: The challenges facing design teams with respect to older and physically disabled people are only now beginning to be addressed, largely due to the fact that the population is ageing. In order for designers to consider the needs of these people and design inclusively, it is necessary to understand the requirements and preferences that are experienced in Activities of Daily Life (ADL), as people interact with everyday products, environments, and systems. This paper presents the results of a survey into the needs of older and disabled people today. The results show that, despite advances in technology and design, participants still have difficulty performing the everyday activities that most of us take for granted.