Systematic exploration of the non-geometric flux landscape

TL;DR

This paper analytically explores the complex flux landscape in type IIB supergravity models, simplifying the scalar potential to classify stable vacua and No-Go scenarios using axionic flux polynomials.

Contribution

It introduces a method using axionic flux polynomials to analytically analyze the flux landscape, significantly simplifying the extremization conditions in a complex supergravity model.

Findings

Over 16,200 configurations lead to No-Go scenarios for stable vacua.

The scalar potential simplifies to around 300 terms depending on 6 moduli and 14 flux parameters.

Systematic classification of flux vacua and No-Go conditions in the studied model.

Abstract

Given the huge size of the generic four-dimensional scalar potentials arising from the type II supergravities based on toroidal orientifolds, it is even hard to analytically solve the extremization conditions, and therefore the previous studies have been mainly focused on taking some numerical approaches. In this work, using the so-called {\it axionic flux polynomials} we demonstrate that the scalar potential and the extremization conditions can be simplified to a great extent, leading to the possibility of performing an analytic exploration of the flux landscape. In this regard, we consider the isotropic case of a type IIB model based on the standard ${\mathbb T}^6/({\mathbb Z}_2 \times {\mathbb Z}_2)$ orientifold having the three-form fluxes $F_3/H_3$ and the non-geometric $Q$-flux. This model results in around 300 terms in the scalar potential which depend on 6 moduli/axionic fields and 14 flux parameters. Considering that the axionic flux polynomials can take either zero or non-zero values results in the need of analyzing $2^{14}=16384$ candidate configurations, and we find that more than 16200 of those result in No-Go scenarios for Minkowskian/de-Sitter vacua. Based on our systematic exploration of non-tachyonic flux vacua, we present a detailed classification of such No-Go scenarios as well as the leftover ``undecided" configurations for which we could not conclude about the presence/absence of the stable Minkowskian/de-Sitter vacua.