One-loop effective potential for the vacuum gauge field in $M_3\times S^3 \times S^1$ space-times

TL;DR

This paper computes the one-loop effective potential for vacuum gauge fields in a specific higher-dimensional space-time, exploring how geometric ratios influence symmetry breaking via the Hosotani mechanism.

Contribution

It provides a detailed calculation of the effective potential in $M_3\times S^3 \times S^1$ and analyzes the impact of the radii ratio on symmetry breaking patterns.

Findings

The effective potential depends on the ratio of $S^1$ and $S^3$ radii.

Symmetry breaking patterns are significantly affected by the geometric parameters.

The results are relevant for models with gauged supergravities and Kaluza-Klein reductions.

Abstract

We calculate the effective potential for the vacuum gauge field from the one-loop matter effect in $M_3\times S^3\times S^1$ space-time. This background geometry is motivated from the recent studies on gauged supergravities with a positive-definite potential, which admits a generalized Kaluza-Klein reduction. We investigate how symmetry breaking patterns through the Hosotani mechanism are affected by the ratio of the radii of $S^1$ and $S^3$.