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We calculate the effective potential for the vacuum gauge field from theone-loop matter effect in $M_3\times S^3\times S^1$ space-time. This backgroundgeometry is motivated from the recent studies on gauged supergravities with apositive-definite potential, which admits a generalized Kaluza-Klein reduction.We investigate how symmetry breaking patterns through the Hosotani mechanismare affected by the ratio of the radii of $S^1$ and $S^3$.Comment: 8pages, 2 figures. RevTeX4; some typos correcte

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

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