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

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 flo...

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Bibliographic Details
Published in:arXiv.org 2008-12
Main Author: Suneeta, V
Format: Article
Language:English
Subjects:
Euclidean geometry
Fixed points (mathematics)
Flow stability
Mathematical analysis
Shell stability
String theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0806.1930