Generalized N=(2,2) Supersymmetric Non-Linear Sigma Models

TL;DR

This paper reformulates N=(2,2) supersymmetric non-linear sigma models using auxiliary superfields on the sum of tangent and cotangent bundles, exploring connections to generalized complex geometry.

Contribution

It introduces a new formulation of the sigma model with auxiliary superfields, linking supersymmetry to generalized complex structures.

Findings

Derived the general form of second supersymmetry in the new formulation.

Connected the model's structure to Hitchin's generalized complex geometry.

Provided insights into the geometric interpretation of supersymmetric sigma models.

Abstract

We rewrite the N=(2,2) non-linear sigma model using auxiliary spinorial superfields defining the model on ${\cal T}\oplus^ *{\cal T}$, where ${\cal T}$ is the tangent bundle of the target space. This is motivated by possible connections to Hitchin's generalized complex structures. We find the general form of the second supersymmetry compatible with that of the original model.