2008/06/30 by V. Suneeta, V Suneeta
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #hep-th #math.DG
paper · pdf · doi:10.1088/0264-9381/26/3/035023
published as Class.Quant.Grav.26:035023,2009 · 29 pages, references added in this version to appear in Classical and Quantum Gravity
arxiv created 2008/12/16 · openalex publication_date 2009/01/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 the geometric stability of (Euclidean) anti-de Sitter ( AdS ) space (i.e., H n ) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of the 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 that this implies its geometric stability with respect to the 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.