Schur correlation functions on $S^3\times S^1$

Understand

The Schur limit of the superconformal index of four-dimensional $\mathcal N=2$ superconformal field theories has been shown to equal the supercharacter of the vacuum module of their associated chiral algebra.

• Applying localization techniques to the theory suitably put on $S^3\times S^1$, we obtain a direct derivation of this fact.
• We also show that the localization computation can be extended to calculate correlation functions of a subset of local operators, namely of the so-called Schur operators.
• Such correlators correspond to insertions of chiral algebra fields in the trace-formula computing the supercharacter.