UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification

TL;DR

This paper explores the possibility of formulating an asymptotically safe, nonperturbatively renormalizable version of the $SU(N)$ Yang-Mills theory in a five-dimensional spacetime with a compact extra dimension, using functional renormalization group techniques.

Contribution

It demonstrates the existence of a nontrivial fixed point for the gauge coupling in the extra-dimensional Yang-Mills theory, suggesting a UV completion via asymptotic safety.

Findings

Existence of a nontrivial fixed point at finite compactification radius.

The gauge coupling flows from an asymptotically safe UV regime to a strong IR limit.

Both gauge coupling and vacuum energy are relevant at the fixed point.

Abstract

The $SU(N)$ Yang-Mills theory in $\mathbb R^4\times S^1$ spacetime is studied as a simple toy model of Gauge-Higgs unification. The theory is perturbatively nonrenormalizable but could be formulated as an asymptotically safe theory, namely a nonperturbatively renormalizable theory. We study the fixed point structure of the Yang-Mills theory in $\mathbb R^4\times S^1$ by using the functional renormalization group in the background field approximation. We derive the functional flow equations for the gauge coupling and the background gauge-field potential. There exists a nontrivial fixed point for both couplings at finite compactification radii. At the fixed point, gauge coupling and vacuum energy are both relevant. The renormalization group flow of the gauge coupling describes the smooth transition between the ultraviolet asymptotically safe regime and the strong interacting infrared limit.