Investigating Off-shell Stability of Anti-de Sitter Space in String Theory

TL;DR

This paper demonstrates the geometric stability of anti-de Sitter space in string theory using Ricci flow analysis, providing a new approach to understanding vacuum stability via world-sheet RG flows.

Contribution

It proves the geometric stability of AdS space under a suitable RG flow, extending stability analysis methods in string theory with mathematical tools from geometric flows.

Findings

AdS space is stable under a specific RG flow.

The stability result extends to Ricci flow via linear stability analysis.

Mathematical tools from geometric flows can be applied to string vacuum stability.

Abstract

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow, and then show this implies its geometric stability with respect to Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.