On the Search for Low $W_0$

TL;DR

This paper develops algorithms to systematically search for type IIB flux vacua with very low superpotential values, analyzing their statistical distribution and implications for phenomenology.

Contribution

It introduces systematic numerical methods for finding low $|W_0|$ vacua and assesses their rarity within the landscape of flux compactifications.

Findings

Low $|W_0|$ vacua are statistically sparse among all flux vacua.

Two-moduli examples illustrate the general findings.

Simple cases show limited tuning freedom for phenomenological use.

Abstract

The magnitude of the vacuum expectation value of the Gukov-Vafa-Witten superpotential $|W_0|$ plays a central role in the phenomenology of type IIB flux compactifications. Recent analytical constructions have shown that perturbatively flat vacua can be used to obtain very low values of $|W_0|$. We present systematic algorithms to carry out exhaustive numerical searches for such vacua. We also analyse them in the statistical context, as part of the entire ensemble of type IIB flux vacua at low $|W_0|$. Our preliminary analysis indicates that these perturbatively flat vacua are statistically sparse in the whole set of vacua at low $|W_0|$ as calculated by Denef and Douglas. Two-moduli examples are used to illustrate these more general findings in specific settings. We find that these simple cases are good examples for existence proofs but they do not feature a large statistical tuning freedom for phenomenological applications.