Classification of Supersymmetric Flux Vacua in M Theory

TL;DR

This paper classifies supersymmetric vacua in M-theory compactifications on seven-dimensional manifolds with fluxes, detailing conditions for various supersymmetry levels and structures, and presenting a new flux-rich N=1 vacuum solution.

Contribution

It provides a comprehensive classification of supersymmetric M-theory vacua with fluxes, including a novel N=1 solution with all fluxes non-zero.

Findings

N=2 vacua with Minkowski space and conformally Kähler base

N=3 and N=4 vacua with specific internal structures

A new N=1 flux vacuum with solved differential equations

Abstract

We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2 structures. In particular, we find for N = 2 supersymmetry, that the external space-time is Minkowski and the base manifold of the internal space is conformally K\"ahler for SU(2) structures, while for SU(3) structures the internal space has to be Einstein-Sasaki and no internal fluxes are allowed. Moreover, we provide a new vacuum with N = 1 supersymmetry and SU(3) structure, where all fluxes are non-zero and the first order differential equations are solved.