$AdS_3 \times S^3$ Background from Poisson-Lie T-Duality

TL;DR

This paper constructs a dual background to $AdS_3 imes S^3$ using Poisson-Lie T-duality, revealing a new asymptotically flat spacetime with potential black hole features, and confirms its supergravity consistency.

Contribution

It applies Poisson-Lie T-duality to generate a novel dual background of $AdS_3 imes S^3$, analyzing its properties and integrability, and verifies supergravity solutions at two-loop order.

Findings

Dual background is asymptotically flat with a black hole interpretation.

The dual model is classically integrable with explicit Lax pairs.

The model satisfies supergravity equations up to two loops.

Abstract

We proceed to construct a dual pair for the $AdS_3 \times S^3$ background by applying non-Abelian T-duality (here as Poisson-Lie (PL) T-duality on a semi-Abelian double). By using a certain parametrization of the $4$-dimensional Lie group ${A}_2 \otimes 2{A}_1$ and by a suitable choice of spectator-dependent matrices, the original $\sigma$-model including the $AdS_3 \times S^3$ metric and a non-trivial $B$-field are constructed. The dual background constructed by means of the PL T-duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non-trivial $H$-flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non-Abelian T-dual $\sigma$-models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two-loop order, and it has been concluded that the resulting model is indeed a solution of supergravity.