Stringy $\mathcal{N}=(2,2)$ holography for AdS${_3}$

TL;DR

This paper proposes a new class of AdS3/CFT2 dualities with (2,2) supersymmetry, demonstrating agreement in BPS spectra and elliptic genus calculations between supergravity, string theory, and the dual CFT.

Contribution

It introduces a novel (2,2) supersymmetric holographic duality involving orbifolds of AdS3 and symmetric product CFTs, with evidence from spectrum and elliptic genus matches.

Findings

BPS spectra from supergravity and string theory match the dual CFT.

Supergravity elliptic genus reproduces the CFT result.

Supports the proposed (2,2) holographic duality.

Abstract

We propose a class of ${\rm AdS}_3/{\rm CFT}_2$ dualities with $\mathcal{N}=(2,2)$ supersymmetry. These dualities relate string theory on ${\rm AdS}_3 \times ({\rm S}^3\times \mathbb{T}^4)/{\rm G}$ to marginal deformations of the symmetric product orbifold of $\mathbb{T}^4/{\rm G}$, where ${\rm G}$ is a dihedral group. We demonstrate that the BPS spectrum calculated from supergravity and string theory agrees with that of the dual CFT. Moreover, the supergravity elliptic genus is shown to reproduce the CFT answer, thus providing further non-trivial evidence in favour of the proposal.