Fermion induced SU(N) Yang-Mills Theory

We study the low energy effects of heavy fermions in an SU(Nc) gauge theory. This talk summarizes the results presented in ref[1] and extends that calculation for lattice regularization. The effect of heavy matter fields at low energies is expected to be no more than an induced effective gauge coupling. This phenomena is well known for lattice Wilson fermions where the fermion doublers induce a shift in the gauge coupling of the order of ∆β ≈ 0.3 for two flavors around β = 5.5. The idea that heavy fermions can induce continuum gauge fields (i.e. the induced gauge coupling βind = ∞) has a long history [2]. In a recent paper it was suggested that one flavor of adjoint scalar fields might induce a continuum gauge theory as well if the mass of the scalar is tuned appropriately [3]. It was argued furthermore that the scalar model can be solved in the large Nc limit. In this paper we calculate the gauge coupling induced by heavy fermions in the fundamental representation and investigate the condition under which the fermions induce a continuum gauge theory. We argue that a necessary condition is that the number of flavors Nf > 11Nc/2 but we cannot prove that it is a sufficient condition as well. We consider the Nf → ∞ sufficient condition here. A: Dimensional regularization. Consider Nf flavor of SU(Nc) fermions with mass M interacting with SU(Nc) gauge fields Wμ. The vacuum functional