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only consider closed strings (open strings enter when we consider D-branes in section 1.4.3). We can choose to make our strings orientable or non- orientable. If a string is orientable, we can tell which way we are travelling along a string. If it is non-orientable, we can’t. There are further choices we can make with respect to the fermionic boundary conditions, and in fact going through every possibility took researchers a lot of time. In the end, there are five consistent superstring theories, summarised in table 1.1. 

What is the spectrum of closed string theory? This is a detailed and complex subject that is visited by many sources (see [9,11,42–45] for exam- ple) so here we just briefly summarise the results. 

The spectrum contains the metric, G$_{µν}$ , the scalar dilaton Φ, and a two index antisymmetric tensor B$_{µν}$ : 

• The metric needs little explanation, and plays the usual role as the device for measuring distance and angles. 

• The dilaton is a very important field in string theory: it generically appears in the action as e $^{Φ}$, and measures the Euler characteristic (the number of holes and handles) of the string worldsheet. Hence the quantity e Φ plays the role of the theory’s coupling. When open 

