Tumbling through a landscape: Evidence of instabilities in high-dimensional moduli spaces

TL;DR

This paper provides numerical evidence that in high-dimensional moduli spaces, vacua become increasingly unstable due to higher tunneling rates, which may limit the diversity of metastable vacua in string theory landscapes.

Contribution

It demonstrates that the tunneling rate increases with the number of scalar fields, suggesting a fundamental instability in high-dimensional moduli spaces.

Findings

Tunneling rates grow rapidly with the number of fields.

The fraction of metastable vacua decreases exponentially with dimension.

Implications for the string theory landscape and dark energy explanation.

Abstract

We argue that a generic instability afflicts vacua that arise in theories whose moduli space has large dimension. Specifically, by studying theories with multiple scalar fields we provide numerical evidence that for a generic local minimum of the potential the usual semiclassical bubble nucleation rate, Gamma = A e^{-B}, increases rapidly as function of the number of fields in the theory. As a consequence, the fraction of vacua with tunneling rates low enough to maintain metastability appears to fall exponentially as a function of the moduli space dimension. We discuss possible implications for the landscape of string theory. Notably, if our results prove applicable to string theory, the landscape of metastable vacua may not contain sufficient diversity to offer a natural explanation of dark energy.