Symmetries of Holographic Minimal Models

TL;DR

This paper identifies the asymptotic symmetry algebra of a higher spin gravity theory dual to minimal model CFTs, showing it matches a family of W-algebras and supports the holographic duality.

Contribution

It establishes the correspondence between the asymptotic symmetry algebra of higher spin theories and W-algebras controlling minimal model CFTs in the 't Hooft limit.

Findings

Asymptotic symmetry algebra matches a family of W-algebras.

W-algebras control the representation theory of minimal model CFTs.

Provides consistency check for the holographic duality.

Abstract

It was recently proposed that a large N limit of a family of minimal model CFTs is dual to a certain higher spin gravity theory in AdS_3, where the 't Hooft coupling constant of the CFT is related to a deformation parameter of the higher spin algebra. We identify the asymptotic symmetry algebra of the higher spin theory for generic 't Hooft parameter, and show that it coincides with a family of W-algebras previously discovered in the context of the KP hierarchy. We furthermore demonstrate that this family of W-algebras controls the representation theory of the minimal model CFTs in the 't Hooft limit. This provides a non-trivial consistency check of the proposal and explains part of the underlying mechanism.