On the geometry of classically integrable two-dimensional non-linear sigma models

TL;DR

This paper derives a master equation linking classical integrability and geometry in 2D non-linear sigma models, revealing new integrable models with spectral parameter-dependent Lax pairs and exploring their relation to T-duality.

Contribution

It introduces a master equation for classical integrability in 2D sigma models and uncovers a new class of integrable models with spectral parameter-dependent Lax pairs.

Findings

A master equation for integrability is established.

A new class of integrable models is discovered.

Connections between integrability and T-duality are highlighted.

Abstract

A master equation expressing the classical integrability of two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. In particular, a closer connection between integrability and T-duality transformations is emphasised. Finally, a whole new class of integrable non-linear sigma models is found and all their corresponding Lax pairs depend on a spectral parameter.