Carolyn Lambert, Vardarajan Suneeta
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 is stable under a wide class of bounded normalizable perturbations satisfying a certain condition. We also present evidence that indicates that the geometry may be stable even on relaxing this condition. Finally, we discuss a result from mathematics that implies the existence of a nonnormalizable mode of the Witten black hole under which the geometry flows to the sausage solution studied by Fateev, Onofri and Zamolodchikov.
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http://arxiv.org/abs/1205.3043
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