# Ultraviolet to Infrared Evolution and Nonperturbative Behavior of ${\rm SU}(N) \otimes {\rm SU}(N-4) \otimes {\rm U}(1)$ Chiral Gauge Theories

## TL;DR

This paper studies the evolution and nonperturbative behavior of complex chiral gauge theories with multiple gauge groups, focusing on their symmetry breaking mechanisms and connections to electroweak symmetry breaking.

## Contribution

It provides a detailed analysis of ${
m SU}(N) imes {
m SU}(N-4) imes {
m U}(1)$ chiral gauge theories, including the lowest case N=6, and explores their symmetry breaking and dynamical properties.

## Key findings

- Theories can exhibit both self-breaking and induced dynamical symmetry breaking.
- Connections are made to electroweak symmetry breaking via fermion condensates.
- Insights into nonperturbative behavior of complex gauge theories are provided.

## Abstract

We analyze the ultraviolet to infrared evolution and nonperturbative properties of asymptotically free ${\rm SU}(N) \otimes {\rm SU}(N-4) \otimes {\rm U}(1)$ chiral gauge theories with $N_f$ copies of chiral fermions transforming according to $([2]_N,1)_{N-4} + ([\bar 1]_N,[\bar 1]_{N-4})_{-(N-2)} + (1,(2)_{N-4})_N$, where $[k]_N$ and $(k)_N$ denote the antisymmetric and symmetric rank-$k$ tensor representations of SU($N$) and the rightmost subscript is the U(1) charge. We give a detailed discussion for the lowest nondegenerate case, $N=6$. These theories can exhibit both self-breaking of a strongly coupled gauge symmetry and induced dynamical breaking of a weakly coupled gauge interaction symmetry due to fermion condensates produced by a strongly coupled gauge interaction. A connection with the dynamical breaking of ${\rm SU}(2)_L \otimes {\rm U}(1)_Y$ electroweak gauge symmetry by the quark condensates $\langle \bar q q\rangle$ due to color SU(3)$_c$ interactions is discussed. We also remark on direct-product chiral gauge theories with fermions in higher-rank tensor representations.