On the Stability of String Theory Vacua

TL;DR

This paper investigates the stability of string theory vacua from a higher-dimensional perspective, showing supersymmetric vacua are stable and exploring potential instabilities in non-supersymmetric cases.

Contribution

It introduces a higher-dimensional approach to analyze vacuum stability, including brane nucleation suppression and positive-energy theorems in M-theory and supergravity.

Findings

Brane bubble nucleation is forbidden in certain compactifications.

Positive-energy theorems can be adapted to higher-dimensional theories.

Non-supersymmetric vacua like skew-whiffed and Englert are not stabilized by natural modifications.

Abstract

Vacuum compactifications may suffer from instabilities under small perturbations or tunnel effects; both are difficult to analyze. In this paper we consider the issue from a higher-dimensional perspective. We first look at how stability works for supersymmetric vacua, where it is widely expected to hold. We first show that the nucleation of brane bubbles in type II AdS compactifications is forbidden in the probe approximation by a simple argument involving pure spinors and calibrations. We then adapt familiar positive-energy theorems directly to M-theory and type II supergravity, rather than to their effective lower-dimensional reductions, also showing how to consistently include localised sources. We finally initiate an analysis of how these arguments might be extended to non-supersymmetric vacua. In M-theory, at the lower-derivative level, we find that the most natural modifications fail to stabilize the skew-whiffed and Englert vacua.