The Large N 't Hooft Limit of Coset Minimal Models

TL;DR

This paper investigates the large N 't Hooft limit of certain 2D minimal models, proposing their duality to higher spin theories in AdS space with scalar fields, extending previous conjectures to new models.

Contribution

It extends the holographic duality proposal to WD_{N/2} and WB_{(N-1)/2} minimal models, analyzing their RG flows and identifying their gravity duals with coupled higher spin and scalar fields.

Findings

Gravity duals are higher spin theories coupled to two massive scalars.

RG flow analysis supports the duality for WD and WB minimal models.

Large N limit described for second parafermion theory model.

Abstract

Recently, Gaberdiel and Gopakumar proposed that the two-dimensional WA_{N-1} minimal model conformal field theory in the large N 't Hooft limit is dual to the higher spin theories on the three-dimensional AdS space with two complex scalars. In this paper, we examine this proposal for the WD_{N/2} and WB_{(N-1)/2} minimal models initiated by Fateev and Lukyanov in 1988. By analyzing the renormalization group flows on these models, we find that the gravity duals in AdS space are higher spin theories coupled to two equally massive real scalar fields. We also describe the large N 't Hooft limit for the minimal model of the second parafermion theory.