Axion minima in string theory

TL;DR

This study investigates the distribution of axion minima in type IIB string theory compactifications, revealing that most geometries have very few minima due to sparse charge matrices, contrasting with more complex potentials.

Contribution

It provides the first large-scale analysis of axion minima distribution across hundreds of thousands of geometries, highlighting the limitations of current models in generating a rich landscape.

Findings

Most geometries have 1-2 axion minima.

Sparse charge matrices lead to few minima despite many instantons.

Rich axion landscapes require varying flux or topology.

Abstract

We study the landscape of axion theories in compactifications of type IIB string theory on orientifolds of Calabi-Yau threefolds. In a sample of approximately 400,000 geometries we find that in the regime of perturbative control there are only a handful of distinct axion minima per geometry, despite there being infinitely many instanton contributions to the potential with unbounded charges. The ensemble we consider has numbers of axion fields ranging from 1 to 491, but the median number of distinct minima is 1, the mean number is 1.9 and the largest is 54. These small numbers of minima occur because the leading axion charge matrix is quite sparse, while the subleading corrections are increasingly exponentially suppressed as the charges increase. On their own, such potentials are nowhere near rich enough to be of interest anthropically. This is in stark contrast to potentials for which the charge matrix is less sparse or the hierarchies between the instanton contributions are less steep, where one can find $\mathcal{O}(10^{500})$ minima for $\mathcal{O}(500)$ axions. To generate a sufficiently large landscape from string compactifications our results indicate that one would need to rely on varying flux or topology, or to develop tools that allow one to go beyond the regime we can control with current techniques.