Conformal Data of Fundamental Gauge-Yukawa Theories

TL;DR

This paper characterizes conformal data such as central charges and critical exponents for fundamental Gauge-Yukawa theories, revealing relations among conformal quantities and extending understanding of free and safe quantum field theories.

Contribution

It provides the first extensive characterization of conformal data for general classes of chiral and vector-like gauge theories, including nonperturbative safe fixed points using conformal perturbation theory.

Findings

Derived relations among conformal data in gauge theories.

Characterized free and safe quantum field theories via conformal data.

Analyzed nonperturbative safe fixed points with large N_f techniques.

Abstract

We determine central charges, critical exponents and appropriate gradient flow relations for nonsupersymmetric vector-like and chiral Gauge-Yukawa theories that are fundamental according to Wilson and that feature calculable UV or IR interacting fixed points. We further uncover relations and identities among the various local and global conformal data. This information is used to provide the first extensive characterisation of general classes of free and safe quantum field theories of either chiral or vector-like nature via their conformal data. Using large $N_f$ techniques we also provide examples in which the safe fixed point is nonperturbative but for which conformal perturbation theory can be used to determine the global variation of the $a$ central charge.