Effective potential analysis for 5D SU(2) gauge theories at finite temperature and radius

Abstract We calculate the one loop effective potential for a 5D SU(2) gauge field theory at finite temperature T = 1 / β and radius R = 1 / M . This calculation is performed, for the first time, in the case of background fields with two constant components A y 3 (directed towards the compact extra dimension with radius R ) and A τ 3 (directed towards the compact Euclidean time with radius β ). This model possesses two discrete symmetries known as Z M ( 2 ) and Z T ( 2 ) . The corresponding phase diagram is presented in [Phys. Lett. B 511 (2001) 269, hep-ph/0104031 ]. However the arguments which lead to this diagram are mainly qualitative. We present a detailed analysis, from our point of view, for this phase diagram, and we support our arguments performing lattice simulations for a simple phenomenological model with two scalar fields interacting through the previously calculated potential.