  The analytic properties of the N = 2 superconformal index are given a
physical interpretation in terms of certain BPS surface defects, which arise as
the IR limit of supersymmetric vortices. The residue of the index at a pole in
flavor fugacity is interpreted as the index of a superconformal field theory
without this flavor symmetry, but endowed with an additional surface defect.
The residue can be efficiently extracted by acting on the index with a
difference operator of Ruijsenaars-Schneider type. By imposing the
associativity constraints of S-duality, we are then able to evaluate the index
of all generalized quiver theories of type A, for generic values of the three
superconformal fugacities, with or without surface defects.

High Energy Physics - Theory