Partition Functions of Holographic Minimal Models

TL;DR

This paper computes the partition function of W_N minimal models in the large N limit and demonstrates a precise match with the spectrum of a 3d higher spin gravity dual, clarifying the role of additional states at finite N.

Contribution

It provides a detailed analysis of the large N limit of W_N minimal models and establishes the exact spectrum correspondence with higher spin gravity, including the decoupling of extra states.

Findings

At infinite N, extra light states become null and decouple.

The spectrum of the boundary CFT matches the bulk higher spin gravity spectrum.

Symmetry considerations support the duality between W_N algebra and higher spin algebra.

Abstract

The partition function of the W_N minimal model CFT is computed in the large N 't Hooft limit and compared to the spectrum of the proposed holographic dual, a 3d higher spin gravity theory coupled to massive scalar fields. At finite N, the CFT contains additional light states that are not visible in the perturbative gravity theory. We carefully define the large N limit, and give evidence that, at N = infinity, the additional states become null and decouple from all correlation functions. The surviving states are shown to match precisely (for all values of the 't Hooft coupling) with the spectrum of the higher spin gravity theory. The agreement between bulk and boundary is partially explained by symmetry considerations involving the conjectured equivalence between the W_N algebra in the large N limit and the higher spin algebra of the Vasiliev theory.