Scale and quality of Peccei-Quinn symmetry and weak gravity conjectures

TL;DR

This paper explores how a hidden gauge symmetry satisfying the weak gravity conjecture can address the quality and hierarchy problems associated with the Peccei-Quinn solution to the strong CP problem, with implications for cosmology.

Contribution

It proposes a simple hidden gauge group framework satisfying the WGC to solve the PQ quality and hierarchy issues, linking Planck-scale physics with cosmological considerations.

Findings

A hidden SU(N) gauge symmetry broken to SO(N) can resolve the problems.

The approach is consistent with the Tower/sub-Lattice WGC.

Cosmological implications are discussed.

Abstract

The promising solution to the strong CP problem by a Peccei-Quinn (PQ) symmetry may introduce quality and hierarchy problems, which are both relevant to Planck physics. In this paper, we study whether both problems can be explained by introducing a simple hidden gauge group that satisfies a weak gravity conjecture (WGC) or its variant. As a concrete example, we point out that a weakly-coupled hidden $SU(N)$ gauge symmetry, which is broken down to $SO(N)$, can do this job in the context of a Tower/sub-Lattice WGC. Cosmology is discussed.