Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-06-11
Class.Quant.Grav.26:035023,2009
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, references added in this version to appear in Classical and Quantum Gravity
Scientific paper
10.1088/0264-9381/26/3/035023
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.
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