Warped Ricci-flat reductions

TL;DR

This paper introduces a class of warped Ricci-flat solutions in supergravity that include de Sitter, anti-de Sitter, and Minkowski vacua, with potential implications for compactification and stability.

Contribution

It presents new explicit warped Ricci-flat solutions with non-trivial warp factors supporting various vacua, and discusses their relation to known supersymmetric reductions.

Findings

Constructed explicit Ricci-flat warped-product solutions supporting (A)dS and Minkowski vacua.

Demonstrated the solutions' relation to maximally supersymmetric sphere reductions.

Found that (A)dS$_3$ vacua in these solutions pass stability tests.

Abstract

We present a simple class of warped-product vacuum (Ricci-flat) solutions to ten and eleven-dimensional supergravity, where the internal space is flat and the warp factor supports de Sitter (dS) and anti-de Sitter (AdS) vacua in addition to trivial Minkowski vacua. We outline the construction of consistent Kaluza-Klein (KK) reductions and show that, although our vacuum solutions are non-supersymmetric, these are closely related to the bosonic part of well-known maximally supersymmetric reductions on spheres. We comment on the stability of our solutions, noting that (A)dS$_3$ vacua pass routine stability tests.