An Index for 2D field theories with large N=4 superconformal symmetry

TL;DR

This paper introduces a new index for 2D theories with large N=4 superconformal symmetry, extending the elliptic genus concept, and explores its implications for the spectrum and AdS/CFT correspondence.

Contribution

It defines a novel index for N=4 theories that constrains non-BPS states and provides a physical interpretation of Hecke operators in this context.

Findings

The index constrains part of the non-BPS spectrum.

Hecke operators are interpreted physically in the theory.

The index is computed explicitly for a symmetric product example.

Abstract

We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum. Motivated by aspects of the AdS/CFT correspondence we study the index in the examples of symmetric product theories. We give a physical interpretation of the Hecke operators which appear in the expressions for partition functions of such theories. Finally, we compute the index for a nontrivial example of a symmetric product theory.