The a theorem for Gauge-Yukawa theories beyond Banks-Zaks
Oleg Antipin, Marc Gillioz, Esben Mølgaard, Francesco Sannino
TL;DR
The paper addresses the a-theorem in four-dimensional nonsupersymmetric gauge–Yukawa theories beyond leading order by constructing the perturbative $\tilde{a}$ function to cubic order using Weyl consistency. It introduces a general Lagrangian with gauge, Yukawa, and scalar quartic interactions and derives the three-loop gauge, two-loop Yukawa, and one-loop quartic beta functions, together with the Weyl-m geometry encoded in $\chi$ and $W$. The authors apply the formalism to a concrete $SU(N_c)$ model with $N_f$ fundamental fermions, adjoint fermions, and a gauge-singlet scalar in the Veneziano limit, revealing Banks–Zaks fixed points and a nontrivial fixed-point merger as parameters vary. They compute the change in $\tilde{a}$, $\Delta\tilde{a}$, between fixed points (e.g., $\Delta\tilde{a}^ ext{BZ}=\mp \chi_{gg}\frac{b_0^2}{b_1^{\text{eff}}}$ at leading order, with three-loop corrections), demonstrating perturbative control in regions and signaling perturbative breakdown near mergers. The work provides a framework to probe RG irreversibility and the structure of fixed points in richer gauge–Yukawa systems, with implications for near-conformal dynamics and beyond.
Abstract
We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including the presence of a merging phenomenon between non-trivial fixed points for which the a theorem has not been tested so far.