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

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