Renormalization-Group Evolution and Nonperturbative Behavior of Chiral Gauge Theories with Fermions in Higher-Dimensional Representations

TL;DR

This paper investigates the nonperturbative behavior and renormalization-group evolution of chiral SU(N) gauge theories with higher-dimensional fermion representations, revealing possible phases and proving anomaly-freedom of effective theories.

Contribution

It provides a general theorem on anomaly cancellation in low-energy effective theories and classifies the phases of chiral gauge theories with symmetric and antisymmetric fermion representations.

Findings

Finite set of theories with k=ℓ=2 analyzed in detail

Possible phases include non-Abelian Coulomb, confinement, or fermion condensation

S_k Ā_k theories with k≥3 are not asymptotically free

Abstract

We study the ultraviolet to infrared evolution and nonperturbative behavior of a simple set of asymptotically free chiral gauge theories with an SU($N$) gauge group and an anomaly-free set of $n_{S_k}$ copies of chiral fermions transforming as the symmetric rank-$k$ tensor representation, $S_k$, and $n_{\bar A_\ell}$ copies of fermions transforming according to the conjugate antisymmetric rank-$\ell$ tensor representation, $\bar A_\ell$, of this group with $k, \ \ell \ge 2$. As part of our study, we prove a general theorem guaranteeing that a low-energy effective theory resulting from the dynamical breaking of an anomaly-free chiral gauge theory is also anomaly-free. We analyze the theories with $k=\ell=2$ in detail and show that there are only a finite number of these. Depending on the specific theory, the ultraviolet to infrared evolution may lead to a non-Abelian Coulomb phase, or may involve confinement with massless composite fermions, or fermion condensation with dynamical gauge and global symmetry breaking. We show that $S_k \bar A_k$ chiral gauge theories with $k \ge 3$ are not asymptotically free. We also analyze theories with fermions in $S_k$ and $\bar A_\ell$ representations of SU($N$) with $k \ne \ell$ and $k, \ \ell \ge 2$.