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.

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.