Effective Potential of Super Yang-Mills theory on M^4\times S^1 and related topics

Abstract

We study the gauge symmetry breaking of an $\mathcal{N}=1$ supersymmetric Yang-Mills theory defined on $M^4\times S^1$, taking correctly account of the vacuum expectation values for the adjoint scalar field $\text{vev}\Sigma$ in vector multiplet in addition to the Wilson line phases $\text{vev}{A}_y$. We evaluate the one-loop effective potential and obtain the vacuum configuration, for which an SU(N) gauge symmetry is not broken. In case of an orbifold $S^1/Z_2$, under appropriate orbifolding boundary conditions, two Higgs doublets are embedded in the zero modes, $A_y^{(0)}$ and ${\Sigma }^{(0)}$. We point out that the tree-level scalar potential resulted from the covariant derivative for the adjoint scalar field is identical to the $D$-term of the MSSM. We also briefly mention the mass spectra of the gauge and Higgs sector in the theory.

Comments: 7 pages, Talk given at 8th European meeting on From the Planck scale to the electroweak scale (PLANCK'05), Trieste, Italy, 23-28 May 2005