Counting Flux Vacua

TL;DR

This paper introduces a method to estimate the expected count of flux vacua in supergravity theories, providing an asymptotic formula for supersymmetric vacua in Calabi-Yau compactifications, especially effective with many fluxes.

Contribution

It develops a novel technique for computing the expected number of vacua in Gaussian supergravity ensembles and derives an asymptotic formula for flux vacua counts in string theory.

Findings

Derived an asymptotic formula for flux vacua count

Provides a practical estimate for vacua in Calabi-Yau compactifications

Applicable in the large flux limit

Abstract

We develop a technique for computing expected numbers of vacua in Gaussian ensembles of supergravity theories, and apply it to derive an asymptotic formula for the index counting all flux supersymmetric vacua with signs in Calabi-Yau compactification of type IIb string theory, which becomes exact in the limit of a large number of fluxes. This should give a reasonable estimate for actual numbers of vacua in string theory, for CY's with small b_3.