Complex structure-induced deformations of sigma-models

TL;DR

This paper introduces a deformation of sigma-models using a B-field related to the Kähler form, preserving integrability and applying it to models like G=S^1 x S^3 and AdS_3 x S^3 x S^1.

Contribution

It presents a novel deformation method for principal chiral models based on complex structures, maintaining zero-curvature equations and extending to superstring backgrounds.

Findings

Deformation preserves integrability via zero-curvature representation.

Explicit example with G=S^1 x S^3 demonstrates the deformation.

Application to AdS_3 x S^3 x S^1 super-sigma-model shows broader relevance.

Abstract

We describe a deformation of the principal chiral model (with an even-dimensional target space G) by a B-field proportional to the K\"ahler form on the target space. The equations of motion of the deformed model admit a zero-curvature representation. As a simplest example, we consider the case of G=S^1 x S^3. We also apply a variant of the construction to a deformation of the AdS_3 x S^3 x S^1 (super-)sigma-model.