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

TL;DR

The paper reframes the strong-$CP$ problem through the topological susceptibility of the QCD vacuum and the physicality of $ heta$-vacua using a Chern-Simons $3$-form, demonstrating that a gauge axion described by a 2-form $B_{ hoeta}$ provides an exact, gravity-compatible solution by Higgsing the $3$-form. It shows that finite $f$ eliminates the CP-violating vacua and that the decoupling limit $f o\

Abstract

The topological susceptibility of the QCD vacuum provides an understanding of $θ$-vacua as vacua of a Chern-Simons gauge theory. In this way, it gives an immediate proof of the physicality of the boundary $θ$-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 $θ$-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.

Figures (3)

• Figure 1: Plot of the domain Wall current $J(z)$ and its derivative $J'(z)$ (normalized w.r.t. $m$).
• Figure 2: A domain wall with a hole in the middle. The cosmic string forms the boundary of the hole.
• Figure 3: A string as the junction between several domain walls.