The phase diagram of Yang-Mills theory with a compact extra dimension

TL;DR

This paper non-perturbatively explores the phase structure of five-dimensional SU(2) Yang-Mills theory with a compact extra dimension, revealing the relationship between gauge field components and mass gaps through lattice simulations.

Contribution

It provides the first detailed non-perturbative phase diagram of 5D Yang-Mills with a compact dimension using lattice regularization and numerical simulations.

Findings

Mapped the phase diagram and identified fixed ratios of gauge field mass to mass gap.

Analyzed the behavior of the theory in different limits and regimes.

Discussed implications for higher-dimensional gauge theories and compactification.

Abstract

We present a non-perturbative study of the phase diagram of SU(2) Yang-Mills theory in a five-dimensional spacetime with a compact extra dimension. The non-renormalizable theory is regularized on an anisotropic lattice and investigated through numerical simulations in a regime characterized by a hierarchy between the scale of low-energy physics, the inverse compactification radius, and the cutoff scale. We map out the structure of the phase diagram and the pattern of lines corresponding to fixed values of the ratio between the mass of the fifth component of the gauge field and the non-perturbative mass gap of the four-dimensional modes. We discuss different limits of the model, and comment on the implications of our findings.