Phase structure and Hosotani mechanism in QCD-like theory with compact dimensions

Abstract

We investigated the phase diagram of SU(3) gauge theory in four dimension with one compact dimension by using the perturbative one-loop effective potential. Effects of the adjoint and fundamental fermions are investigated and then the rich phase structure in the quark-mass and compactsize scale is realized. Our results are qualitatively consistent with the recent lattice calculation and clearly show that the lattice calculation can be understood from the Hosotani mechanism. Moreover, we show the result obtained by using the flavor twisted boundary condition for fundamental fermion which does not break the Z 3 symmetry, explicitly.

Symmetry breaking caused by large ℛ-charge

“…One naive way is to use the lattice gauge theory. The mechanism have been studied already by lattice gauge theories [16,17,18,19,20,21]. For example, in [17,18], they studied the SU(3) gauge symmetry in the 3+1 dimensional flat spacetime.…”