  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.
