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

TL;DR

This paper investigates the stability of the Euclidean Witten black hole under Ricci flow, finding no unstable normalizable modes but discussing a non-normalizable mode leading to a different geometric solution.

Contribution

It provides a linearized stability analysis of the Witten black hole and connects mathematical results to physical flow behavior.

Findings

No unstable normalizable modes found

Existence of a non-normalizable mode leading to sausage geometry

Stability confirmed for circularly symmetric perturbations

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.