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We propose an investigation of stability of vacua in string theory bystudying their stability with respect to a (suitable) world-sheetrenormalization group (RG) flow. We prove geometric stability of (Euclidean)anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplestRG flow in closed string theory, the Ricci flow. AdS space is not a fixed pointof Ricci flow. We therefore choose an appropriate flow for which it is a fixedpoint, 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. Wealso discuss tools from the mathematics of geometric flows that can be used tostudy stability of string vacua.

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