Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem

TL;DR

This paper explores a novel approach to the strong CP problem using non-invertible Peccei-Quinn symmetries from fractional instantons in a specific gauge theory, proposing a massless quark solution compatible with the Standard Model.

Contribution

It introduces non-invertible Peccei-Quinn symmetries arising from fractional instantons in a gauge theory with a unique global structure, leading to a new massless quark solution to the strong CP problem.

Findings

Identifies non-invertible symmetries linked to fractional instantons.

Proposes a UV $SU(9)$ theory for quark color-flavor unification.

Demonstrates generation of CKM structure and CP violation without disrupting the solution.

Abstract

We consider theories of gauged quark flavor and identify non-invertible Peccei-Quinn symmetries arising from fractional instantons when the resulting gauge group has non-trivial global structure. Such symmetries exist solely because the Standard Model has the same numbers of generations as colors, $N_g = N_c$. This leads us to a massless down-type quark solution to the strong CP problem in an ultraviolet $SU(9)$ theory of quark color-flavor unification. We show how the CKM flavor structure and weak CP violation can be generated without upsetting our solution.