Generalized Superconformal Index for Three Dimensional Field Theories

TL;DR

This paper generalizes the superconformal index for 3D theories by incorporating background gauge fields with magnetic flux, enabling the matching of indices for dual theories and advancing the understanding of mirror symmetry.

Contribution

It introduces a new generalized superconformal index that includes magnetic flux backgrounds, facilitating the study of dualities in three-dimensional field theories.

Findings

Successfully matches superconformal indices for dual theories

Demonstrates the gauging of global symmetries at the index level

Provides a new tool for analyzing 3D mirror symmetry

Abstract

We introduce a generalization of the S^2 x S^1 superconformal index where background gauge fields with magnetic flux are coupled to the global symmetries of the theory. This allows one to gauge a global symmetry at the level of the index, which we use to show the matching of the superconformal index for N=2 SQED with N_f flavors and its mirror dual.