A uniqueness theorem for warped $N>16$ Minkowski backgrounds with fluxes

TL;DR

This paper proves that warped Minkowski backgrounds with more than 16 supersymmetries in 11D and 10D supergravity are locally equivalent to the maximally supersymmetric Minkowski vacuum, regardless of field smoothness.

Contribution

It establishes a uniqueness theorem showing such highly supersymmetric warped backgrounds are locally isometric to flat Minkowski space, extending previous classifications.

Findings

All such backgrounds are locally isometric to Minkowski space.

They have the same local geometry as the maximally supersymmetric vacuum.

The result holds even when fields are not smooth everywhere.

Abstract

We demonstrate that warped Minkowski space backgrounds, $\mathbb{R}^{n-1,1}\times_w M^{d-n}$, $n\geq3$, that preserve strictly more than 16 supersymmetries in $d=11$ and type II $d=10$ supergravities and with fields which may not be smooth everywhere are locally isometric to the $\mathbb{R}^{d-1,1}$ Minkowski vacuum. In particular, all such flux compactification vacua of these theories have the same local geometry as the maximally supersymmetric vacuum $\mathbb{R}^{n-1,1}\times T^{d-n}$.