Comments on N = 2 supersymmetric sigma models in projective superspace

TL;DR

This paper clarifies the formulation of the most general off-shell N=2 supersymmetric sigma model in projective superspace, highlighting the universal symplectic structure linked to hyperkahler geometry.

Contribution

It provides a model-independent expression for the holomorphic symplectic two-form that governs the second supersymmetry transformation in these models.

Findings

Derived a universal expression for the holomorphic symplectic form.

Connected the symplectic form to the hyperkahler structure of the target space.

Clarified the role of complex structures in supersymmetric sigma models.

Abstract

For the most general off-shell N = 2 supersymmetric sigma model in projective superspace, we elaborate on its formulation in terms of N = 1 chiral superfields. A universal (model-independent) expression is obtained for the holomorphic symplectic two-form, which determines the second supersymmetry transformation. This two-form is associated with the two complex structures of the hyperkahler target space, which are complimentary to the one used to realize the target space as a Kahler manifold.