Complete classification of Minkowski vacua in generalised flux models

TL;DR

This paper systematically classifies Minkowski vacua in type II orientifold supergravity models with generalised fluxes, revealing stable and unstable solutions, including those requiring non-geometric fluxes, and analyzing their properties and parameter space behavior.

Contribution

It provides a complete classification of Minkowski extrema in these models, including stable de Sitter vacua, using a mix of analytic and numerical methods, extending previous algebraic and no-go theorem analyses.

Findings

Existence of Minkowski vacua with tachyonic directions.

Stable Minkowski/de Sitter minima in specific algebraic models.

Vacua interpolate between singular points where moduli go to zero or infinity.

Abstract

We present a complete and systematic analysis of the Minkowski extrema of the N=1, D=4 Supergravity potential obtained from type II orientifold models that are T-duality invariant, in the presence of generalised fluxes. Based on our previous work on algebras spanned by fluxes, and the so-called no-go theorems on the existence of Minkowski and/or de Sitter vacua, we perform a partly analytic, partly numerical analysis of the promising cases previously hinted. We find that the models contain Minkowski extrema with one tachyonic direction. Moreover, those models defined by the Supergravity algebra so(3,1)^2 also contain Minkowski/de Sitter minima that are totally stable. All Minkowski solutions, stable or not, interpolate between points in parameter space where one or several of the moduli go to either zero or infinity, the so-called singular points. We finally reinterpret our results in the language of type IIA flux models, in order to show explicitly the contribution of the different sources of potential energy to the extrema found. In particular, the cases of totally stable Minkowski/de Sitter vacua require of the presence of non-geometric fluxes.