Higher axion strings

A bstract We study the minimal requirements to obtain axion strings for axions with exponentially good quality. These ingredients appear in theories where an axion coming from a higher-form gauge field mixes with the phase of a complex scalar field. The resulting axion is perturbatively massless and inherits a high-quality shift symmetry from the global higher-form symmetry while being compatible with a post-inflationary axion scenario. Axions produced in this manner share features of both extra-dimensional and ordinary axions but are ultimately distinct from either. We refer to such axions as higher axions , as the mechanism responsible for the mixing is that of higher-groups. We present a simple toy model on a 5-dimensional manifold with boundary. The boundary hosts the complex scalar that provides axion strings through standard mechanisms. In addition, we study how these scenarios may arise in heterotic and type II string theory compactifications.