The integrable harmonic map problem versus Ricci flow

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.