ONE-LOOP EFFECTIVE POTENTIAL FOR THE VACUUM GAUGE FIELD IN M3×S3×S1 SPACETIME

We calculate the effective potential for the vacuum gauge field from the one-loop matter effect in M3×S3×S1 spacetime. 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 S1 and S3.