Orbifold Schur Index and IR formula

TL;DR

This paper explores the orbifold version of the Schur index in supersymmetric theories, proposing a generalized IR formula and testing its validity in different contexts, revealing successes and limitations.

Contribution

It introduces a general formula for the orbifold Schur index in Lagrangian theories and proposes a generalized IR formula, extending previous work.

Findings

The generalized IR formula matches free hypermultiplet systems with orbifold invariance.

Disagreement arises for theories with dynamical vector multiplets.

The paper provides a framework for calculating orbifold Schur indices in supersymmetric theories.

Abstract

We discuss orbifold version of the Schur index defined as the supersymmetric partition function in S^3/Z_n x S^1. We first give a general formula for Lagrangian theories obtained by localization technique, and then suggest a generalization of the Cordova and Shao's IR formula. We confirm the generalized IR formula gives the correct answer for systems with free hypermultiplets if we tune the background fields so that they are invariant under the orbifold action. Unfortunately, we find disagreement for theories with dynamical vector multiplets.