The strong CP problem and higher dimensional gauge theories

TL;DR

This paper proposes a higher-dimensional gauge theory framework with an axion-like field to naturally address the strong CP problem, revealing a novel periodic Chern-Simons term that modifies traditional axion solutions.

Contribution

It introduces a new scenario where the Chern-Simons term is radiatively generated as a periodic function of the Wilson-loop phase, offering a novel approach to the strong CP problem.

Findings

The CS term is 1-loop exact and UV-finite.

The CS term is a periodic function of the Wilson-loop phase.

Modification of axion solutions to the strong CP problem.

Abstract

We discuss a natural scenario to solve the strong CP problem in the framework of the higher dimensional gauge theory. An axion-like field $A_y$ has been built-in as the extra-space component of the higher dimensional gauge field. The coupling of $A_y$ with gluons is attributed to the radiatively induced "Chern-Simons" (CS) term. We adopt a toy model with some unknown gauge symmetry U(1)$_X$. The CS term is obtained in two ways: first by a concrete 1-loop calculation and next by use of the Fujikawa's method to deal with the chiral anomaly in 4D space-time. The obtained results are identical, which implies that the radiative correction to the CS term is "1-loop exact" and is also free from UV-divergence even though the theory itself is non-renormalizable. As a novel feature of this scenario, such obtained CS term is no longer linear in the field $A_y$ as in the usually discussed CS term in 5D space-time but a periodic function of $A_y$, since $A_y$ has a physical meaning as the Wilson-loop phase. We argue how such novel feature of this scenario causes the modification of the ordinary solutions of the strong CP problem based on the axion fields.