The Strong-$CP$ Problem and its Gauge Axion solution as Evidence for Fundamental Strings

TL;DR

This paper proposes a gauge axion solution to the strong-$CP$ problem, linking it to fundamental strings and gravity, and explores its topological and string-theoretic properties.

Contribution

It introduces a gauge axion as a novel solution to the strong-$CP$ problem that is UV-complete within a fundamental theory of gravity, connecting axions, strings, and gravity.

Findings

Gauge axion is a pure gauge two-form field.

Strings sourcing the gauge axion are fundamental in gravity theories.

Absence of the axion quality problem suggests a link to fundamental strings.

Abstract

The topological susceptibility of the QCD vacuum provides an understanding of $\theta$-vacua as vacua of a Chern-Simons gauge theory. In this way, it gives an immediate proof of the physicality of the boundary $\theta$-term. This makes the essence of the strong-$CP$ puzzle very transparent and offers a solution in form of the gauge axion, which has exact quality. This axion represents an intrinsic part of the QCD gauge redundancy without any reference to an anomalous global symmetry. It is a two-form transforming under the QCD gauge symmetry. Due to its pure gauge nature, the gauge axion represents a powerful tool to monitor physics of $\theta$-vacua in various regimes. Unlike the ordinary Peccei-Quinn axion, which is UV-completed into a Goldstone phase of a complex scalar and thereby suffers from the quality problem, the gauge axion is UV-completed directly into a fundamental theory of gravity. We study the domain wall and string structure of the gauge axion and show that the strings sourcing it must be a part of this fundamental theory. We thus observe that the absence of the axion quality problem motivates the presence of fundamental strings. This provides a new argument for a connection between the axion and gravity.