QCD on a Tree

TL;DR

This paper introduces a mean field model for lattice QCD and chiral fields that exhibits phase transitions, generalizing known models and providing insights into large N critical regimes.

Contribution

It proposes a new mean field approximation model for lattice QCD that captures phase transitions and relates to multi-matrix models, extending the Gross-Witten transition.

Findings

Identifies a phase transition between strong and weak coupling phases.

Establishes an equivalence to multi-matrix models for U(N) gauge groups.

Generalizes the Gross-Witten phase transition to broader regimes.

Abstract

A model is proposed which can be regarded as a mean field approximation for pure lattice QCD and chiral field. It always possesses a phase transition between a strong coupling phase (where it reduces to a one-plaquette integral) and a non-trivial weak coupling one. For the U(N) gauge group, it is equivalent to some multi-matrix model. This analogy allows for determining possible large N critical regimes thus generalizing the Gross-Witten phase transition in the one-plaquetee model.