On Asymptotic safety in 4D gauge theory with additional dimension=4 operators

TL;DR

This paper investigates the existence and properties of interacting fixed points in a four-dimensional $SU(N_c)$ gauge theory with fermions and scalars, revealing stable conformal phases and detailed perturbative calculations up to four loops.

Contribution

It identifies a new conformal fixed point in a 4D gauge theory with scalars and fermions, including stability analysis and anomalous dimensions, using high-order perturbation theory.

Findings

Discovery of an interacting conformal fixed point with stable vacua.

Calculation of anomalous dimensions and operator scaling up to four loops.

Analysis of scalar operators and phase crossovers in the theory.

Abstract

We study interacting fixed points of simple quantum field theory in four-dimensional $SU(N_c)$ coupled to $N_f$ species of color fermions and $N_f^2$ colorless scalars in the Veneziano limit. Using the rich structure of all possible quartic scalar operators, we find an interacting conformal fixed point with stable vacua and crossovers inbetween. We perform calculations in perturbation theory up to four loop in the gauge and three loop in the Yukawa and scalar couplings. We also consider anomalous dimensions for fields, scalar mass squared, and a class of dimension-three operators.