Fermions and Goldstone bosons in an asymptotically safe model

Understand

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.