The integrable harmonic map problem versus Ricci flow

2012/05/31 by Sergei L. Lukyanov, Sergei L Lukyanov · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Curvature #Dilaton #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Harmonic map #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Quantum mechanics #Renormalization #Ricci curvature #Ricci flow #Sigma model #Torsion (gastropod) #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/j.nuclphysb.2012.08.002

published as RUNHETC-2012-10 · 24 pages

arxiv created 2012/06/17 · openalex publication_date 2012/08/08 · arxiv updated 2015/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We construct a zero-curvature representation for a four-parameter family of non-linear sigma models with a Kalb-Ramond term. The one-loop renormalization is performed that gives rise to a new set of ancient and eternal solutions to the Ricci flow with torsion. Our analysis provides an explicit illustration of the role of the dilaton field for the renormalization of the non-linear sigma model.

Citations

• Nonlinear Models in2+εDimensions
• Three-manifolds with positive Ricci curvature
• Non-abelian bosonization in two dimensions
• Torsion and geometrostasis in nonlinear sigma models
• Ricci flow with surgery on three-manifolds

Cited by

• Twists of trigonometric sigma models
• On the Yang-Baxter Poisson algebra in non-ultralocal integrable systems
• Supergravity backgrounds for deformations of AdSn×Sn supercoset string models

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