Twisted holography on AdS$_3 \times S^3 \times K3 $ & the planar chiral algebra

TL;DR

This paper explores twisted holography for AdS3×S3×K3, identifying the dual chiral algebra in the planar limit and demonstrating how symmetries fix certain correlation functions, with potential for perturbative corrections.

Contribution

It provides a detailed analysis of twisted supergravity on AdS3×S3×K3, deriving the planar chiral algebra and demonstrating symmetry constraints on correlation functions.

Findings

Derived the planar chiral algebra for the dual CFT

Fixed 2 and 3-point functions using symmetries

Outlined a method for perturbative corrections in 1/N

Abstract

In this work, we revisit and elaborate on twisted holography for AdS$_3 \times S^3 \times X$ with $X= T^4$, K3, with a particular focus on K3. We describe the twist of supergravity, identify the corresponding (generalization of) BCOV theory, and enumerate twisted supergravity states. We use this knowledge, and the technique of Koszul duality, to obtain the $N \rightarrow \infty$, or planar, limit of the chiral algebra of the dual CFT. The resulting symmetries are strong enough to fix planar 2 and 3-point functions in the twisted theory or, equivalently, in a 1/4-BPS subsector of the original duality. This technique can in principle be used to compute corrections to the chiral algebra perturbatively in $1/N$.