Renormalization-Group Evolution of Chiral Gauge Theories

TL;DR

This paper investigates the renormalization-group flow of specific chiral gauge theories with SU(N) symmetry, analyzing their infrared behavior, condensate formation, and degrees of freedom, providing new insights into their evolution.

Contribution

It constructs and studies three novel chiral gauge theories with detailed beta function analysis and verifies a conjectured inequality on field degrees of freedom across parameter ranges.

Findings

Infrared zeros of beta functions identified for the theories.

Predictions made for fermion condensate formation channels.

Theories satisfy a conjectured inequality on degrees of freedom.

Abstract

We calculate the ultraviolet to infrared evolution and analyze possible types of infrared behavior for several asymptotically free chiral gauge theories with gauge group SU($N$) and massless chiral fermions transforming according to a symmetric rank-2 tensor representation $S$ and $N+4$ copies (flavors) of a conjugate fundamental representation $\bar F$, together with a vectorlike subsector with chiral fermions in higher-dimensional representation(s). We construct and study three such chiral gauge theories. These have respective vectorlike subsectors comprised of (a) $p$ copies of fermions in the adjoint representation, (b) $N = 2k$ even and $p$ copies of fermions in the antisymmetric rank-$k$ tensor representation, and (c) $p$ copies of $\{S + \bar S\}$ fermions. Results are presented for beta functions, their infrared zeros, and predictions from the most-attractive-channel approach for the formation of bilinear fermion condensates. Importantly, we show that for these theories, the expected ultraviolet to infrared evolution obeys a conjectured inequality concerning the field degrees of freedom for all values of the parameters $N$ and $p$ characterizing each theory.