General N = 1 Supersymmetric Flux Vacua of (Massive) Type IIA String Theory

TL;DR

This paper derives conditions for  supersymmetric flux vacua in massive type IIA string theory, showing they require nearly-Kf6hler internal geometry, with fluxes proportional to the mass parameter and a fixed dilaton, resulting in a small negative cosmological constant.

Contribution

It provides the first explicit conditions linking supersymmetric flux vacua to nearly-Kf6hler geometry in massive type IIA string theory.

Findings

Flux vacua exist only with nearly-Kf6hler internal geometry.

Fluxes are proportional to the mass parameter.

The dilaton is fixed by quantized flux ratios.

Abstract

We derive conditions for the existence of four-dimensional \N=1 supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist only when the internal geometry is nearly-K\"ahler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.