Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories

الأصل · EN

In equivariantly gauge-fixed SU(N) Yang--Mills theories, the gauge symmetry is only partially fixed, leaving a subgroup H⊂ SU(N) unfixed. Such theories avoid Neuberger's nogo theorem if the subgroup H contains at least the Cartan subgroup U(1)ⁿ⁻¹, and they are thus non-perturbatively well defined if regulated on a finite lattice. We calculate the one-loop beta function for the coupling g²=ξg², where g is the gauge coupling and ξ is the gauge parameter, for a class of subgroups including the cases that H=U(1)ⁿ⁻¹ or H=SU(M)× SU(N-M)× U(1). The coupling g represents the strength of the interaction of the gauge degrees of freedom associated with the coset SU(N)/H. We find that g, like g, is asymptotically free. We solve the renormalization-group equations for the running of the couplings g and g, and find that dimensional transmutation takes place also for the coupling g, generating a scale Λ which can be larger than or equal to the scale Λ associated with the gauge coupling g, but not smaller. We speculate on the possible implications of these results.