Effective potential for a covariantly constant gauge field in curved spacetime

TL;DR

This paper investigates how gravitational effects influence the stability of chromomagnetic vacua by calculating the one-loop effective potential in curved spacetimes, revealing curvature-induced phase transitions and stabilization effects.

Contribution

It provides the first calculation of the one-loop effective potential for a covariantly constant SU(2) gauge field in curved spacetime, demonstrating curvature-induced phase transitions and stabilization.

Findings

Curvature can induce phase transitions between different chromomagnetic vacua.

Gravitational effects can stabilize the chromomagnetic vacuum by eliminating the imaginary part of the potential.

Numerical results show stabilization occurs at certain curvatures.

Abstract

We discuss the influence of gravitational effects on the stabilization of the chromomagnetic vacuum. The one-loop effective potential for a covariantly constant SU(2) gauge field in ${\bf S}^2 \times {\bf R}^2$ and ${\bf T}^2 \times {\bf R}^2$ is calculated. A possibility of curvature-induced phase transitions between zero and nonzero chromomagnetic vacua is found ---what is also confirmed through the calculation of the renormalization group (RG) improved effective potential on constant-curvature spaces with small curvature. Numerical evaluation indicates that for some curvatures the imaginary part of the effective potential disappears (gravitational stabilization of the chromomagnetic vacuum occurs).