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

**Authors:** Sergei Gukov, Emil Martinec, Gregory Moore, Andrew Strominger  
**arXiv:** [hep-th/0404023](https://arxiv.org/abs/hep-th/0404023)  
**Date:** 2004-04-02  
**Summary page:** https://www.summarizepaper.com/en/paper/hep-th--0404023v2/

## Key points

- Paper focuses on families of theories with large N=4 superconformal symmetry
- Introduces a new index that generalizes the elliptic genus of theories with N=2 symmetry
- New index can constrain part of the non-BPS spectrum
- Study conducted in the context of symmetric product theories, motivated by AdS/CFT correspondence
- Provides physical interpretation of Hecke operators in partition functions of symmetric product theories
- Computes index for a nontrivial example, demonstrating applicability and usefulness
- Contributes to understanding field theories with large N=4 superconformal symmetry and their connections to AdS/CFT correspondence

## Summary

This paper focuses on families of theories with large N=4 superconformal symmetry. The authors introduce a new index that generalizes the elliptic genus of theories with N=2 symmetry. Unlike the N=2 case, this new index has the ability to constrain part of the non-BPS spectrum. Motivated by aspects of the AdS/CFT correspondence, the authors study this index in the context of symmetric product theories. They provide a physical interpretation of the Hecke operators that appear in the expressions for partition functions of such theories. In addition, the authors compute the index for a nontrivial example of a symmetric product theory, demonstrating its applicability and usefulness in practical scenarios. Overall, this paper contributes significantly to our understanding of field theories with large N=4 superconformal symmetry by introducing a new index and exploring its properties in various examples. The results obtained shed light on important aspects of these theories and their connections to other areas such as AdS/CFT correspondence.