A holographic dual for string theory on $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1$

TL;DR

This paper proposes a holographic duality between string theory on a specific AdS3 background and a symmetric orbifold CFT, providing detailed BPS spectrum matches that support the duality's validity.

Contribution

It identifies the dual CFT as the symmetric orbifold of the alS_ theory and confirms the BPS spectrum correspondence with supergravity and world-sheet calculations.

Findings

BPS spectrum of the symmetric orbifold matches supergravity results.

World-sheet theory's BPS spectrum aligns with the supergravity spectrum.

Strong evidence supporting the proposed holographic duality.

Abstract

The CFT dual of string theory on $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1$ is conjectured to be the symmetric orbifold of the $\mathcal{S}_\kappa$ theory, provided that one of the two $Q_5^\pm$ quantum numbers is a multiple of the other. We determine the BPS spectrum of the symmetric orbifold in detail, and show that it reproduces precisely the BPS spectrum that was recently calculated in supergravity. We also determine the BPS spectrum of the world-sheet theory that is formulated in terms of WZW models, and show that, apart from some gaps (which are reminiscent of those that appear in the corresponding $\mathbb{T}^4$ calculation), it also reproduces this BPS spectrum. In fact, the matching seems to work as well as for the familiar $\mathbb{T}^4$ case, and thus our results give strong support for this proposal.