Asymptotic safety and the gauged SU(N) nonlinear sigma-model
M. Fabbrichesi, R. Percacci, A. Tonero, O. Zanusso
TL;DR
This paper investigates the renormalization group flow of a gauged SU(N) nonlinear sigma-model in higher dimensions, identifying fixed points that influence the model's unitarity and scattering properties.
Contribution
It provides a detailed analysis of the beta functions and fixed points of the gauged SU(N) nonlinear sigma-model, highlighting the asymptotic safety scenario in dimensions greater than two.
Findings
Gaussian fixed point for gauge coupling
Non-Gaussian fixed point for Goldstone boson coupling
Fixed point influences unitarity and scattering amplitudes
Abstract
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. Attention is paid to the gauge- and scheme-dependence of the results.
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