Asymptotic safety and the gauged SU(N) nonlinear sigma-model

We study the beta functions of the leading, two-derivative terms of the left-gauged SU(N) nonlinear sigma-model in d dimensions. In d>2, we find the usual Gaussian ultraviolet fixed point for the gauge coupling and an attractive non-Gaussian fixed point for the Goldstone boson coupling. The position of the latter fixed point controls the chiral expansion, unitarity and the strength of the tree-level Goldstone boson scattering amplitudes. For large N the model is weakly coupled, unitary at all energies and well described by the lowest order of chiral perturbation theory. Attention is payed to the gauge- and scheme-dependence of the results.