Triality in Minimal Model Holography

TL;DR

This paper explores the quantum structure of the W_{}[] symmetry algebra in minimal model holography, revealing a triality among three parameter values that explains symmetry matches and impacts bulk scalar field interpretations.

Contribution

It determines the quantum symmetry algebra structure at finite central charge and uncovers a triality linking three distinct parameter regimes in minimal model holography.

Findings

Identifies an exact triality in the W_{}[] algebra at quantum level.

Explains symmetry correspondence between minimal models and higher spin theories.

Proposes a non-perturbative origin for one bulk scalar field.

Abstract

The non-linear W_{\infty}[\mu] symmetry algebra underlies the duality between the W_N minimal model CFTs and the hs[\mu] higher spin theory on AdS_3. It is shown how the structure of this symmetry algebra at the quantum level, i.e. for finite central charge, can be determined completely. The resulting algebra exhibits an exact equivalence (a`triality') between three (generically) distinct values of the parameter \mu. This explains, among other things, the agreement of symmetries between the W_N minimal models and the bulk higher spin theory. We also study the consequences of this triality for some of the simplest W_{\infty}[\mu] representations, thereby clarifying the analytic continuation between the`light states' of the minimal models and conical defect solutions in the bulk. These considerations also lead us to propose that one of the two scalar fields in the bulk actually has a non-perturbative origin.