Vector Models in the Singlet Sector at Finite Temperature

TL;DR

This paper investigates the thermal behavior of the O(N) vector scalar theory in 2+1 dimensions, revealing a high-temperature phase transition linked to the bulk Planck scale in the dual higher spin gravity framework.

Contribution

It provides the first analysis of the finite temperature phase transition in the singlet sector of the O(N) vector model, connecting it to the dual gravity description.

Findings

A large N transition occurs at temperature ~√N.

The transition indicates a reduction in degrees of freedom.

Relations among invariants modify the expected higher spin gas behavior.

Abstract

We study the thermal properties of the O(N) vector-like scalar theory in the singlet sector in 2+1 dimensions. This theory is conjectured to be the AdS/CFT dual of Vasiliev higher spin gravity. We find that a large N transition occurs but only at a very high temperature of order \sqrt{N}. This corresponds to the bulk Planck energy. The transition signals a decrease in the number of degrees of freedom from that expected in the simple higher spin gas, due to relations among the O(N) bilinear invariants.