Properties of hyperkahler manifolds and their twistor spaces

TL;DR

This paper explores the mathematical structures linking hyperkahler manifolds, supersymmetric sigma-models, projective superspace, and twistor space, providing a comprehensive review and new insights into their interrelations.

Contribution

It offers a coherent synthesis of existing concepts with new results clarifying the connections between hyperkahler geometry and supersymmetric theories.

Findings

Clarified the relationship between supersymmetric sigma-models and hyperkahler manifolds

Presented new results on the structure of twistor spaces associated with hyperkahler manifolds

Reviewed the role of projective superspace in describing these geometric structures

Abstract

We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.