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

Understand

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.