# A "Gauged" $U(1)$ Peccei-Quinn Symmetry

## TL;DR

This paper proposes a simple mechanism embedding the Peccei-Quinn global symmetry into a gauged $U(1)$, providing a plausible origin for the PQ symmetry in solving the strong $CP$ problem.

## Contribution

It introduces a straightforward method to derive the PQ symmetry from a gauged $U(1)$, enhancing theoretical understanding of its origin.

## Key findings

- The mechanism can be implemented in various models with PQ symmetry.
- It offers a new perspective on the origin of the PQ symmetry.
- The approach simplifies the embedding of the PQ symmetry in gauge theories.

## Abstract

The Peccei-Quinn (PQ) solution to the strong $CP$ problem requires an anomalous global $U(1)$ symmetry, the PQ symmetry. The origin of such a convenient global symmetry is quite puzzling from the theoretical point of view in many aspects. In this paper, we propose a simple prescription which provides an origin of the PQ symmetry. There, the global $U(1)$ PQ symmetry is virtually embedded in a gauged $U(1)$ PQ symmetry. Due to its simplicity, this mechanism can be implemented in many conventional models with the PQ symmetry.