On the phase structure of extra-dimensional gauge theories with fermions

We study the phase structure of five-dimensional Yang-Mills theories coupled to Dirac fermions. In order to tackle their non-perturbative character, we derive the flow equations for the gauge coupling and the effective potential for the Aharonov-Bohm phases employing the Functional Renormalisation Group. We analyse the infrared and ultraviolet fixed-point solutions in the flow of the gauge coupling as a function of the compactification radius of the fifth dimension. We discuss various types of trajectories which smoothly connect both dimensional limits. Last, we investigate the phase diagram and vacuum structure of the gauge potential for different fermion content.