New $AdS_3 \times S^2$ T-duals with $\mathcal{N} = (0,4)$ supersymmetry

TL;DR

The paper constructs explicit $AdS_3 \times S^2$ geometries with $\mathcal{N}=(0,4)$ supersymmetry by applying non-Abelian T-duality to known near-horizon backgrounds and uplifting to 11D, obtaining the first explicit $SU(2)$-structure example and a new background outside prior classifications. It analyzes the holographic duals by computing central charges and identifying brane configurations (color and flavor) and their instanton/baryon vertex realizations, revealing a consistent large-$\mathcal{N}=(0,4)$ CFT structure with two affine current algebras. A second, related construction starts from $AdS_3 \times S^3_+ \times S^3_- \times S^1$ and, after non-Abelian T-duality and Abelian dualities, yields a massive IIA → massless IIA uplift to 11D, further supporting a rich landscape of $AdS_3$ solutions in 11D with $SU(2)$-structure. The results clarify how non-Abelian T-duality reshapes charges and isometries, provide concrete brane realizations for the dual CFTs, and point to a broader, potentially compactification-friendly class of $AdS_3$ solutions beyond current classifications.

Abstract

It is well known that Hopf-fibre T-duality and uplift takes the D1-D5 near-horizon into a class of $AdS_3 \times S^2$ geometries in 11D where the internal space is a Calabi-Yau three-fold. Moreover, supersymmetry dictates that Calabi-Yau is the only permissible $SU(3)$-structure manifold. Generalising this duality chain to non-Abelian isometries, a strong parallel exists, resulting in the first explicit example of a class of $AdS_3 \times S^2$ geometries with $SU(2)$-structure. Furthermore, the non-Abelian T-dual of $AdS_3 \times S^3 \times S^3 \times S^1$ results in a new supersymmetric $AdS_3 \times S^2$ geometry, which falls outside of all known classifications. We explore the basic properties of the holographic duals associated to the new backgrounds. We compute the central charges and show that they are compatible with a large $\mathcal{N}=4$ superconformal algebra in the infra-red.