Asymptotic safety and the gauged SU(N) nonlinear σ model

We study the beta functions of the leading, two-derivative terms of the left-gauged SU(N) nonlinear σ 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 paid to the gauge and scheme dependence of the results. © 2011 The American Physical Society