The integrable harmonic map problem versus Ricci flow

TL;DR

This paper constructs a zero-curvature representation for certain non-linear sigma models, analyzes their one-loop renormalization, and presents new solutions to Ricci flow with torsion, highlighting the role of the dilaton field.

Contribution

It introduces a zero-curvature framework for sigma models with a Kalb-Ramond term and derives new Ricci flow solutions with torsion, emphasizing the dilaton's role in renormalization.

Findings

New solutions to Ricci flow with torsion

Explicit role of the dilaton in renormalization

Zero-curvature representation for sigma models

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.