The Large N 't Hooft Limit of Coset Minimal Models

TL;DR

The paper investigates a broad class of nonunitary and unitary coset minimal models WD$_n^{(p)}$ and WB$_n^{(p)}$ in the large $N$ 't Hooft limit, extending the Gaberdiel–Gopakumar duality to higher- spin AdS$_3$ gravity. By performing RG analyses of perturbations and computing conformal dimensions and central charges, it demonstrates that these CFTs flow from $D_n^{(p)}$ to $D_n^{(p-1)}$ (and analogously for $B_n$-type models), with the bulk dual described by a higher spin theory in AdS$_3$ coupled to two real scalars of dimensions $1-\\lambda$ and $1+\\lambda$ (mass $M^2=-(1-\\lambda^2)$). The total bulk partition function matches the boundary partition function through higher-spin contributions and scalar determinants, supporting a consistent AdS$_3$/CFT$_3$ correspondence for these models. The work further discusses the second parafermion family, potential supersymmetric extensions, and outlines open problems for gravity duals of generalized coset theories, highlighting a fertile path for non-supersymmetric AdS$_3$ holography.

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.