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

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.