# Accidental Peccei-Quinn symmetry protected to arbitrary order

## TL;DR

This paper proposes a gauge theory framework where an accidental $U(1)$ symmetry, protected to arbitrary order, naturally solves the strong CP problem via a Peccei-Quinn mechanism or yields axion-like particles, depending on the vacuum configuration.

## Contribution

It introduces a novel gauge theory setup with scalar and fermion fields that protect an accidental $U(1)$ symmetry to arbitrary order, providing new solutions to the strong CP problem and axion-like particle models.

## Key findings

- Protection of $U(1)$ symmetry up to order $N$ for $N>4$
- Two vacuum configurations with different symmetry breaking patterns
- Possible realization of Peccei-Quinn solution and axion-like particles

## Abstract

A $SU(N)_L\times SU(N)_R$ gauge theory for a scalar multiplet $Y$ transforming in the bi-fundamental representation $(N,\bar N)$ preserves, for $N>4$, an accidental $U(1)$ symmetry firstly broken at operator dimension $N$. Two configurations are possible for the vacuum expectation value of $Y$, which correspond to the (maximal) little groups $\mathcal{H}_s=SU(N)_{L+R}$ and $\mathcal{H}_h=SU(N-1)_L\times SU(N-1)_R\times U(1)_{L+R}$. In the first case the accidental $U(1)$ gets also broken, yielding a pseudo Nambu-Goldstone boson with mass suppression controlled by $N$, while in the second case a global $U(1)$ remains unbroken. The strong CP problem is solved by coupling $Y$ to new fermions carrying color. The first case allows for a Peccei-Quinn solution with $U(1)_{PQ}$ protected up to order $N$ by the gauge symmetry. In the second case $U(1)$ can get broken by condensates of the new strong dynamics, resulting in a composite axion. By coupling $Y$ to fermions carrying only weak isospin, models for axion-like particles can be constructed.