A localising AdS$_3$ sigma model

TL;DR

This paper constructs a simplified, tensionless AdS$_3$ sigma model with unique correlation functions, providing new insights into holography and dualities beyond traditional WZW models.

Contribution

It introduces a novel CFT at $k=3$ with localised correlators, differing from standard WZW models, and explores its implications for holographic dualities in AdS$_3$ backgrounds.

Findings

Three-point functions feature momentum-conserving delta functions.

Higher-point functions localise to covering map configurations.

The theory applies to both supersymmetric and bosonic AdS$_3$ backgrounds.

Abstract

We construct a CFT with $\mathfrak{sl}(2,\mathbb{R})_k$ symmetry at the `tensionless' point $k=3$, which is distinct from the usual $\mathrm{SL}(2,\mathbb{R})_{k=3}$ WZW model. This new CFT is much simpler than the generic WZW model: in particular its three-point functions feature momentum-conserving delta functions, and its higher-point functions localise to covering map configurations in moduli space. We establish the consistency of the theory by explicitly deriving the four-point function from the three-point data via a sum over conformal blocks. The main motivation for our construction comes from holography, and we show that various simple supersymmetric holographic dualities for $k_{\rm s}=1$ ($k=3$) can be constructed by replacing the $\mathrm{AdS}_3$ factor on the worldsheet with this alternative theory. This includes in particular the prototypical case of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathbb{T}^4$, as well as the recently discussed example of $\mathrm{AdS}_3 \times \mathrm{S}^3 \times \mathrm{S}^3 \times \mathrm{S}^1$. However, our analysis does not require supersymmetry and also applies to bosonic ${\rm AdS}_3$ backgrounds (at $k=3$).