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

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.

29 pages, references added in this version to appear in Classical and Quantum Gravity

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Cited by in corpus (3)

• Local Conformal Instability and Local Non-Collapsing in the Ricci flow of Quantum Spacetime
• Investigating stability of a class of black hole spacetimes under Ricci flow
• A proposal for studying off-shell stability of vacuum geometries in string theory