# 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.

## Key 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.

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Source: https://tomesphere.com/paper/hep-lat/9509092