The superconformal index of N=1 class S fixed points

We investigate the superconformal index of four-dimensional N=1 superconformal field theories that arise on coincident M5 branes wrapping a holomorphic curve in a local Calabi-Yau three-fold. The structure of the index is very similar to that which appears in the special case preserving N=2 supersymmetry. We first compute the index for the fixed points that admit a known four-dimensional ultraviolet description and prove infrared equivalence at the level of the index for all such constructions. These results suggest a formulation of the index as a two-dimensional topological quantum field theory that generalizes the one that computes the N=2 index. The TQFT structure leads to an expression for the index of all class S fixed points in terms of the index of the N=2 theories. Calculations of spectral data using the index suggests a connection between these families of fixed points and the mathematics of SU(2) Yang-Mills theory on the wrapped curve.

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