Compactification on negatively curved manifolds

TL;DR

This paper demonstrates that compactifying string/M theory on negatively curved manifolds requires either significant warping, large stringy corrections, or both, to achieve maximally symmetric space-times.

Contribution

It establishes necessary conditions for string/M theory compactifications on negatively curved manifolds, highlighting the need for warping or corrections.

Findings

Significant warping is required for such compactifications.

Large stringy corrections are necessary in these scenarios.

Maximally symmetric space-times cannot be achieved without these features.

Abstract

We show that string/M theory compactifications to maximally symmetric space-times using manifolds whose scalar curvature is everywhere negative, must have significant warping, large stringy corrections, or both.