Analytics of type IIB flux vacua and their mass spectra

TL;DR

This paper studies the properties and mass spectra of flux vacua in type IIB string theory compactifications, providing analytic descriptions of their features and classifying vacua into three types.

Contribution

It introduces an analytic framework for understanding flux vacua with quadratic superpotentials, classifies vacua into three categories, and derives explicit expressions for their mass spectra.

Findings

Supersymmetric vacua have at least one flat direction.

Analytic formulas for vacuum expectation values and masses are derived.

Enables generation of large ensembles of flux vacua in specific Calabi-Yau geometries.

Abstract

We analyze the tree-level potential of type IIB flux compactifications in warped Calabi-Yau orientifolds, in regions of weak coupling and moderately large complex structure. In this regime, one may approximate the flux-induced superpotential $W$ by a polynomial on the axio-dilaton and complex structure fields, and a significant fraction of vacua corresponds to a quadratic $W$. In this quadratic case, we argue that vacua fall into three classes, for which one can push the analytic description of their features. In particular, we provide analytic expressions for the vacuum expectation values and flux-induced masses of the axio-dilaton and complex structure fields in a large subclass of vacua, independently of the Calabi-Yau and the number of moduli. We show that supersymmetric vacua always contain flat directions, at least at this level of approximation. Our findings allow to generate vast ensembles of flux vacua in specific Calabi-Yau geometries, as we illustrate in a particular example.