Hyperkahler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace

TL;DR

This paper constructs four-dimensional N=2 supersymmetric sigma models on tangent bundles of classical Hermitian symmetric spaces using projective superspace, and derives hyperkahler metrics on their cotangent bundles.

Contribution

It introduces a method to explicitly build hyperkahler structures on cotangent bundles of Hermitian symmetric spaces via projective superspace techniques.

Findings

Explicit construction of N=2 models on tangent bundles

Derivation of hyperkahler metrics on cotangent bundles

Application to classical Hermitian symmetric spaces

Abstract

Kahler manifolds have a natural hyperkahler structure associated with (part of) their cotangent bundles. Using projective superspace, we construct four-dimensional N = 2 models on the tangent bundles of some classical Hermitian symmetric spaces (specifically, the four regular series of irreducible compact symmetric Kahler manifolds, and their non-compact versions). A further dualization yields the Kahler potential for the hyperkahler metric on the cotangent bundle.