Calculating the Superconformal Index and Seiberg Duality

TL;DR

This paper introduces methods to compute the superconformal index in four-dimensional theories, enabling tests of Seiberg duality and RG flows, and proposing related mathematical identities.

Contribution

It develops a novel technique to calculate the superconformal index for 4D superconformal theories, applicable to dualities and RG flows.

Findings

Validated the index calculation for theories with non-trivial RG flows

Confirmed the index invariance under Seiberg duality

Proposed new group/number theoretical identities

Abstract

We develop techniques to calculate an index for four dimensional superconformal field theories. This superconformal index is counting BPS operators which preserve only one supercharge. To calculate the superconformal index we quantize the field theory on S^3 X R and show that the twisted theory has an appropriate mass gap. This allows for the interactions to be switched off continuously without the superconformal index being changed. We test those techniques for theories which go through a non-trivial RG flow and for Seiberg dual theories. This leads to the conjecture of some group/number theoretical identities.