# Gauge-Yukawa theories: Beta functions at large ${N}_{f}$

Antipin, Oleg (Rudjer Boskovic Institute, Division of Theoretical Physics, Bijenička 54, HR-10000 Zagreb, Croatia) ; Dondi, Nicola Andrea (CP3-Origins, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark) ; Sannino, Francesco (CP3-Origins, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark) ; Thomsen, Anders Eller (CP3-Origins, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark) ; Wang, Zhi-Wei (CP3-Origins, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark) (Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada)

06 July 2018

Abstract: We consider the dynamics of gauge-Yukawa theories in the presence of a large number of matter constituents. We first review the current status for the renormalization group equations of gauge-fermion theories and extend the results to semisimple groups. In this regime these theories develop an interacting ultraviolet fixed point that for the semisimple case leads to a rich phase diagram. The latter contains a complete asymptotically safe fixed point repulsive in all couplings. We then add two gauged Weyl fermions belonging to arbitrary representations of the semisimple gauge group and a complex, gauged scalar to the original gauge-fermion theory allowing for new Yukawa interactions and quartic scalar self-coupling. Consequently, we determine the first nontrivial order in $1/{N}_{f}$ for the Yukawa and quartic beta functions. Our work elucidates, consolidates, and extends results obtained earlier in the literature. We also acquire relevant knowledge about the dynamics of gauge-Yukawa theories beyond perturbation theory. Our findings are applicable to any extension of the standard model featuring a large number of fermions such as asymptotic safety.

Published in: Physical Review D 98 (2018)