Large N Elliptic Genus and AdS/CFT Correspondence

TL;DR

This paper computes the elliptic genus of a boundary superconformal field theory in the AdS_3/CFT_2 correspondence, finding exact agreement with a sigma model on K3^N/S_N, thus supporting the duality.

Contribution

It provides the first supergravity calculation of the elliptic genus for this duality, confirming the match with the sigma model result.

Findings

Exact agreement of elliptic genus with sigma model on K3^N/S_N

Introduction of an exclusion principle yields a finite quantity

Supports the AdS_3/CFT_2 duality in the supergravity regime

Abstract

According to one of Maldacena's dualities, type IIB string theory on AdS_3 X S^3 X K3 is equivalent to a certain N=(4,4) superconformal field theory. In this note we compute the elliptic genus of the boundary theory in the supergravity approximation. A finite quantity is obtained once we introduce a particular exclusion principle. In the regime where the supergravity approximation is reliable, we find exact agreement with the elliptic genus of a sigma model with target space K3^N/S_N.