Fermions and Goldstone bosons in an asymptotically safe model

TL;DR

This paper investigates the renormalization group flow of a model with Goldstone bosons and fermions, revealing conditions for UV fixed points and implications for asymptotically safe theories of weak interactions.

Contribution

It demonstrates how fermion loops affect the existence of non-Gaussian fixed points and explores the role of four-fermion interactions in restoring asymptotic safety.

Findings

Non-Gaussian UV fixed point is lost due to fermion loops unless N is large.

Adding four-fermion interactions yields multiple non-Gaussian fixed points.

Predicted contact interaction strengths are compared with experimental bounds.

Abstract

We consider a model in which Goldstone bosons, described by a SU(N) chiral nonlinear sigma model, are coupled to an N-plet of colored fermions by means of a Yukawa interaction. We study the one-loop renormalization group flow and show that the non-Gaussian UV fixed point, which is present in the purely bosonic model, is lost because of fermion loop effects unless N is sufficiently large. We then add four-fermion contact interactions to the lagrangian and show that in this case there exist several non-Gaussian fixed points. The strength of the contact interactions, predicted by the requirement that the theory flows towards a fixed point in the UV, is compared to the current experimental bounds. This toy model could provide an important building block of an asymptotically safe model of the weak interactions.