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

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 Ay3 (directed towards the compact extra dimension with radius R) and Aτ3 (directed towards the compact Euclidean time with radius β). This model possesses two discrete symmetries known as ZM(2) and ZT(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.