On the U(2) Lattice Gauge Theory

TL;DR

This paper investigates the phase structure of U(2) lattice gauge theory with a simple action, identifying a first-order transition line and providing evidence for the continuum limit in the weak coupling regime.

Contribution

It determines the phase diagram of U(2) lattice gauge theory with a specific action and analyzes the nature of the phase transition and continuum limit.

Findings

Identification of a first-order critical line passing through the U(1) critical point.

Derivation of the order parameter for the first-order transition.

Evidence supporting the continuum limit in the weak coupling regime.

Abstract

We study the U(2) lattice gauge theory in the pure gauge sector using the simplest action, with determinant and fundamental terms, having the naive continuum limit of SU(2)$\times$U(1). We determine part of the phase diagram of the model and find a first-order critical line which goes through the U(1) critical point. We show how to deduce both the order parameter of the first-order transition and the U(2) renormalization group flow from the lattice potential in the determinant and fundamental representations. We give evidence that a Monte-Carlo simulation of the model is indeed consistent with the symmetric SU(2)$\times$U(1) continuum limit in the weak coupling pertubative regime.