Effective potential for a covariantly constant gauge field in curved spacetime

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 ${\mathbf{S}}^2\times {\mathbf{R}}^2$ and ${\mathbf{T}}^2\times {\mathbf{R}}^2$ 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).

accepted in Phys. Rev. D