Stability analysis of the Witten black hole (cigar soliton) under world-sheet RG flow

Abstract

We analyze the stability of the Euclidean Witten black hole (the cigar soliton in mathematics literature) under first-order RG (Ricci) flow of the world-sheet sigma model. This analysis is from the target space point of view. We find that the Witten black hole has no unstable normalizable perturbative modes in a linearized mode analysis in which we consider circularly symmetric perturbations. Finally, we discuss a result from mathematics that implies the existence of a non-normalizable mode of the Witten black hole under which the geometry flows to the sausage solution studied by Fateev, Onofri and Zamolodchikov.

17 pages, version to appear in Physical Review D, and now has complete proof of stability for circularly symmetric perturbations, in response to referee comments

References in corpus (7)

• A new approach to static numerical relativity, and its application to Kaluza-Klein black holes
• Ricci flow and black holes
• Closed String Tachyon Condensation: An Overview
• On sigma model RG flow, "central charge" action and Perelman's entropy
• Remarks on Black Hole Instabilities and Closed String Tachyons
• The Fixed Points of RG Flow with a Tachyon
• Eternal Solutions to the Ricci Flow on ${\mathbb{R}}^2$

Cited by in corpus (2)

• $T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory
• The sausage sigma model revisited