A semi-local holographic minimal model

TL;DR

This paper conjectures the spectrum of operators in the W(N) minimal model and proposes a semi-local higher spin gauge theory on AdS3 x S^1 as its holographic dual, with broken symmetries due to boundary conditions.

Contribution

It introduces a novel semi-local higher spin gauge theory dual to the W(N) minimal model, with detailed conjectures on the spectrum and boundary condition effects.

Findings

Conjectured the complete spectrum of single-trace operators.

Proposed a semi-local higher spin gauge theory as the holographic dual.

Identified symmetry breaking due to boundary conditions on S^1.

Abstract

We present a conjecture on the complete spectrum of single-trace operators in the infinite N limit of W(N) minimal model and evidences for the conjecture. We further propose that the holographic dual of W(N) minimal model in the 't Hooft limit is an unusual "semi-local" higher spin gauge theory on AdS3 x S^1. At each point on the S^1 lives a copy of three-dimensional Vasiliev theory, that contains an infinite tower of higher spin gauge fields coupled to a single massive complex scalar propagating in AdS3. The Vasiliev theories at different points on the S^1 are correlated only through the AdS3 boundary conditions on the massive scalars. All but one single tower of higher spin symmetries are broken by the boundary conditions.