A survey of large N continuum phase transitions

TL;DR

This survey reviews large N continuum phase transitions in QCD, discussing symmetry breaking, Wilson loops, topology, and connections to string theory, highlighting recent progress and universality properties.

Contribution

It provides a comprehensive overview of phase transitions in large N gauge theories, including new insights into Wilson loops, topology, and relations to string theory.

Findings

Identification of cascade of phase transitions with symmetry breaking

Universality properties of Wilson loops as a function of area

Connections between large N gauge theories and string theory

Abstract

The main focus of this talk is the physics of large N QCD on a continuum torus. A cascade of phase transitions associated with the breaking of U(1) symmetries will be discussed. The continuum Wilson loop as a function of its area will be discussed along with its universality properties and the associated double scaling limit. Some recent progress in twisted Eguchi-Kawai is presented. Gauge field topology and $\theta$ vacuua are also discussed in the context of large N gauge theories. Phase transitions in 2D large N principal chiral models are compared with similar transitions in large $N$ gauge theories. Finally, connections to some topics in string theory and gravity are briefly described.