Finding all flux vacua in an explicit example

TL;DR

This paper explicitly constructs all supersymmetric flux vacua in a specific Calabi-Yau compactification of type IIB string theory using polynomial homotopy continuation, confirming statistical predictions and analyzing flux tuning effects.

Contribution

It provides a complete enumeration of flux vacua in a concrete example, applying polynomial homotopy continuation and exploring implications for cosmological constant tuning.

Findings

Number of vacua matches statistical predictions

Flux tuning can adjust the cosmological constant

Range of moduli and gravitino masses verified

Abstract

We explicitly construct all supersymmetric flux vacua of a particular Calabi-Yau compactification of type IIB string theory for a small number of flux carrying cycles and a given D3-brane tadpole. The analysis is performed in the large complex structure region by using the polynomial homotopy continuation method, which allows to find all stationary points of the polynomial equations that characterize the supersymmetric vacuum solutions. The number of vacua as a function of the D3 tadpole is in agreement with statistical studies in the literature. We calculate the available tuning of the cosmological constant from fluxes and extrapolate to scenarios with a larger number of flux carrying cycles. We also verify the range of scales for the moduli and gravitino masses recently found for a single explicit flux choice giving a K\"ahler uplifted de Sitter vacuum in the same construction.