# Vacuum Structure of Yang-Mills Theory in Curved Spacetime

## TL;DR

This paper investigates the stability of the chromomagnetic vacuum in Yang-Mills theory within curved spacetime, specifically analyzing how positive curvature influences vacuum stability through heat trace calculations.

## Contribution

It provides the first detailed analysis of the chromomagnetic vacuum stability in curved spacetime using heat trace methods on product spaces.

## Key findings

- Chromomagnetic vacuum stability depends on radii and field strengths.
- Stability is achieved under specific curvature and parameter conditions.
- Heat trace calculations confirm vacuum stability in certain regimes.

## Abstract

The stability of the chromomagnetic Savvidy vacuum in QCD under the influence of positive Riemannian curvature is studied. The heat traces of the operators relevant to SO(2) gauge-invariant Yang-Mills fields and Faddeev-Popov ghosts are calculated on product spaces of S^2 and S^1 \times S^1. It is shown that the chromomagnetic vacuum with covariantly constant chromomagnetic field is stable in a certain set of radii and field strengths.