Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry

TL;DR

This paper develops N=2 supersymmetric sigma models with tangent and cotangent bundle target spaces over quadrics, utilizing the projective superspace formalism to explore models with SO(n) symmetry.

Contribution

It introduces a novel construction of N=2 supersymmetric sigma models on (co)tangent bundles over quadrics using projective superspace, expanding the class of models with SO(n) isometry.

Findings

Constructed explicit models on tangent and cotangent bundles over Q^{n-2}

Applied projective superspace for off-shell N=2 supersymmetry

Enhanced understanding of sigma models with SO(n) symmetry

Abstract

We construct N=2 supersymmetric nonlinear sigma models whose target spaces are tangent as well as cotangent bundles over the quadric surface Q^{n-2} = SO(n)/[SO(n-2)\times U(1)]. We use the projective superspace framework, which is an off-shell formalism of N=2 supersymmetry.