Minkowski flux vacua of type II supergravities

TL;DR

This paper characterizes a broad class of Minkowski flux vacua in type II supergravities, using a sum-of-squares approach that does not depend on supersymmetry, and proposes an extension to non-geometric fluxes.

Contribution

It introduces a sum-of-squares framework for Minkowski flux vacua that captures solutions without relying on supersymmetry, and suggests an extension to non-geometric fluxes.

Findings

Characterization of Minkowski flux vacua via sum-of-squares method.

Solutions automatically satisfy 10d equations of motion when squares are zero.

Proposal of an extension to include non-geometric fluxes.

Abstract

We study flux compactifications of 10d type II supergravities to 4d Minkowski space-time, supported by parallel orientifold Op-planes with 3 $\leq$ p $\leq$ 8. With some restrictions, the 4d Ricci scalar can be written as a negative sum of squares involving BPS-like conditions. Setting all squares to zero provides automatically a solution to 10d equations of motion. This way, we characterize a broad class, if not the complete set, of Minkowski flux vacua. We also conjecture an extension to include non-geometric fluxes. None of our results rely on supersymmetry.