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

TL;DR

This work investigates whether reformulating a 2D ${\cal N}=(2,2)$ supersymmetric non-linear sigma model on the enlarged target $T \oplus^* T$ with auxiliary spinorial fields $\Psi_\pm$ can reveal a richer target-space geometry, potentially connected to generalized complex geometry. By deriving the most general second supersymmetry compatible with the original model using a 1.5 order formalism and symmetry constraints, the authors show the on-shell transformations are fully determined by the original complex structures $J^{(\pm)}$, the metric $G$, and the B-field $B$; the analysis includes special limits such as the pure Poisson sigma model when the metric vanishes and a Buscher-type duality under isometries. The results imply a close link between the generalized complex geometric framework and ${\cal N}=(2,2)$ supersymmetry in two dimensions, while leaving open questions about the zero-metric limit, potential ${\cal N}=(2,1)$ extensions, and boundary conditions for open models. Overall, the paper provides a rigorous bridge between auxiliary-field sigma models on $T \oplus^* T$ and generalized complex geometry, with concrete transformations and duality rules anchored in the original geometric data.

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.