Convexity, large charge and the large-N phase diagram of the $\varphi^4$ theory

TL;DR

This paper explores the phase diagram of the O(2N) vector model with quadratic and quartic interactions across different dimensions, revealing distinct behaviors and a new metastable phase at high energies.

Contribution

It applies large charge methods to analyze the large-N effective potential in dimensions 2<D<4 and 4<D<6, uncovering different phase behaviors and a metastable phase.

Findings

In 2<D<4, the theory is well-behaved.

In 4<D<6, the model leads to a complex CFT in the UV.

A new metastable massive phase is identified at high energy on the cylinder.

Abstract

In this note we discuss the phase space of the O(2N) vector model in the presence of a quadratic and a quartic interaction by writing the large-N effective potential using large charge methods in dimensions 2<D<4 and 4<D<6. Based on a simple discussion of the convexity properties of the grand potential, we find very different behavior in the two regimes: while in 2<D<4, the theory is well-behaved, the model in 4<D<6 leads to a complex CFT in the UV, consistently with earlier results. We also find a new metastable massive phase in the high-energy regime for the theory on the cylinder.