Abstract
We study $\mathrm{SU}(N)$ supersymmetric Yang-Mills theory with massless adjoint matter defined on ${M}^{3}\ensuremath{\bigotimes}{S}^{1}.$ The $\mathrm{SU}(N)$ gauge symmetry is broken maximally to ${U(1)}^{N\ensuremath{-}1},$ independent of the number of flavor and the boundary conditions of the fields associated with the Scherk-Schwarz mechanism of supersymmetry breaking. The mass of the Higgs scalar is generated through quantum corrections in the extra dimension. The quantum correction can become manifest by a finite Higgs boson mass at low energies even in the limit of small extra dimensions thanks to the supersymmetry breaking parameter of the Scherk-Schwarz mechanism.
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