# Dynamics and symmetries in chiral $SU(N)$ gauge theories

## TL;DR

This paper investigates the dynamics and symmetry breaking patterns in four-dimensional chiral $SU(N)$ gauge theories, using anomaly matching and proposing a new mass hierarchy conjecture related to symmetry breaking.

## Contribution

It extends previous work by analyzing symmetry realization in chiral gauge theories with new conjectures on mass hierarchies and dynamics constrained by anomaly matching.

## Key findings

- Severe constraints on dynamics from anomaly matching.
- Identification of color-flavor locking and Abelianization mechanisms.
- Proposal of a novel mass hierarchy generation in chiral theories.

## Abstract

Dynamics and symmetry realization in various chiral gauge theories in four dimensions are investigated, generalizing a recent work by M. Shifman and the present authors, by relying on the standard 't Hooft anomaly matching conditions and on some other general ideas. These requirements are so strong that the dynamics of the systems are severely constrained. Color-flavor or color-flavor-flavor locking, dynamical Abelianization, and combinations of these, are powerful ideas which often leads to solutions of the anomaly matching conditions. Moreover, a conjecture is made on generation of a mass hierarchy associated with symmetry breaking in chiral gauge theories, which has no analogues in vector-like gauge theories such as QCD.