Index for three dimensional superconformal field theories with general R-charge assignments

TL;DR

This paper develops a general formula for the superconformal index of 3D N=2 theories with arbitrary R-charges using localization, and verifies it through mirror symmetry examples.

Contribution

It introduces a new, comprehensive index formula applicable to a broad class of 3D N=2 superconformal theories with arbitrary R-charge assignments.

Findings

Derived a universal index formula using localization.

Confirmed mirror symmetry by matching indices in mirror pairs.

Validated the formula with explicit computations.

Abstract

We derive a general formula of an index for three dimensional N=2 superconformal field theories with general R-charge assignments to chiral multiplets by using the localization method in S^2xS^1 background. As examples we compute the index for theories in a few mirror pairs, and confirm the agreement of the indices in each mirror pair.