Symmetry breaking from Scherk-Schwarz compactification

Abstract

We analyze the classical stable configurations of an extra-dimensional gauge theory, in which the extra dimensions are compactified on a torus. Depending on the particular choice of gauge group and the number of extra dimensions, the classical vacua compatible with four-dimensional Poincaré invariance and zero instanton number may have zero energy. For SU(N) on a two-dimensional torus, we find and catalogue all possible degenerate zero-energy stable configurations in terms of continuous or discrete parameters, for the case of trivial or non-trivial 't Hooft non-abelian flux, respectively. We then describe the residual symmetries of each vacua.

24 pages, 1 figure, Section 4 modified

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• One-loop effective potential in M4 x T2 with and without 't Hooft flux
• CP violation from pure gauge in extra dimensions