Three-Form Gauging of axion Symmetries and Gravity

TL;DR

This paper reformulates axion and certain Standard Model symmetries as gauge theories involving three-form fields, providing new insights into the strong CP problem, gravitational effects, and the stability of axion solutions.

Contribution

It introduces a three-form gauge field framework for understanding axion symmetries and gravity's impact on the strong CP problem, offering a novel perspective on symmetry breaking and vacuum structure.

Findings

Reformulation of axion and anomalous symmetries as three-form gauge theories.

Identification of gravitational effects as potential threats to axion solutions.

Insight into how additional massless three-forms can reintroduce the strong CP problem.

Abstract

Nonlinearly realized Abelian global symmetries can be reformulated as local shift symmetries gauged by three-form gauge fields. The anomalous symmetries of the Standard Model (such as Peccei-Quinn or $B+L$) can be dualized to local symmetries gauged by the Chern-Simons three-forms of the Standard Model gauge group. In this description the strong CP problem can be reformulated as the problem of a massless three-form field in QCD, which creates an arbitrary CP-violating constant four-form electric field in the vacuum. Both the axion as well as the massless quark solutions amount to simply Higgsing the three-form gauge field, hence screening the electric field in the vacuum. This language gives an alternative way for visualizing the physics of the axion solution as well as the degree of its vulnerability due to gravitational corrections. Any physics that can jeopardize the axion solution must take the QCD three-form out of the Higgs phase. This can only happen if the physics in question provides an additional massless three-form. The axion then Higgses one combination of the three-forms and the QCD electric field gets partially unscreened, reintroducing the strong CP problem. Gravity provides such a candidate in form of the Chern-Simons spin connection three-form, which could un-Higgs the QCD three-form in the absence of additional chiral symmetries. We also discuss analogous effects for the baryon number symmetry.