Stability of the (two-loop) Renormalization Group Flow for Nonlinear Sigma Models

Abstract

We prove the stability of the torus, and with suitable rescaling, hyperbolic space under the (two-loop) renormalization group flow for the nonlinear sigma model. To prove stability we use similar techniques to \cite{GIK02}, where the stability of the torus under Ricci flow was first established. The main technical tool is maximal regularity theory.

May differ slightly from the published version

References in corpus (4)

• A Gradient Flow for Worldsheet Nonlinear Sigma Models
• On sigma model RG flow, "central charge" action and Perelman's entropy
• Irreversibility of World-sheet Renormalization Group Flow
• A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First Order

Cited by in corpus (8)

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• On higher order geometric and renormalisation group flows
• Higher order geometric flows on three dimensional locally homogeneous spaces
• Short-time existence for the second order renormalization group flow in general dimensions
• The Wasserstein geometry of non-linear sigma models and the Hamilton-Perelman Ricci flow