$\mathcal{N}=(3,3)$ holography on ${\rm AdS}_3 \times ({\rm S}^3 \times {\rm S}^3 \times {\rm S}^1)/\mathbb Z_2$

TL;DR

This paper proposes a new AdS$_3$/CFT$_2$ duality involving a $ abla=(3,3)$ supersymmetric background with a $ ext{S}^3 imes ext{S}^3 imes ext{S}^1/ ext{Z}_2$ geometry, matching BPS spectra and elliptic genera.

Contribution

It introduces a novel holographic duality between string theory on a specific orbifold background and a symmetric product orbifold CFT, with detailed spectral and elliptic genus matching.

Findings

BPS spectra of string theory and CFT match exactly.

Elliptic genus computations agree between supergravity and CFT.

Supports the proposed $ abla=(3,3)$ holographic duality.

Abstract

We consider string theory on AdS$_3$ $\times$ (S$^3$ $\times$ S$^3$ $\times$ S$^1)/\mathbb Z_2$, a background supporting $\mathcal N=(3,3)$ spacetime supersymmetry. We propose that string theory on this background is dual to the symmetric product orbifold of $\mathcal S_0/\mathbb Z_2$ where $\mathcal S_0$ is a theory of four free fermions and one free boson. We show that the BPS spectra of the two sides of the duality match precisely. Furthermore, we compute the elliptic genus of the dual CFT and that of the supergravity limit of string theory and demonstrate that they match, hence providing non-trivial support for the holographic proposal.