Relating harmonic and projective descriptions of N=2 nonlinear sigma models

TL;DR

This paper unifies the harmonic and projective descriptions of N=2 nonlinear sigma models by establishing a Hamiltonian framework that links their structures and provides explicit solutions for specific hyperkahler target spaces.

Contribution

It extends the relationship between harmonic and projective superspaces to general nonlinear sigma models, introducing a unifying action framework.

Findings

Unified harmonic and projective descriptions via a single action.

Derived projective solutions from harmonic solutions for Taub-NUT and Eguchi-Hanson.

Demonstrated the natural emergence of Hamiltonian and symplectic structures from the unifying action.

Abstract

Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian structure of the harmonic action and the symplectic structure of the projective action naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkahler target spaces. For the two examples of Taub-NUT and Eguchi-Hanson, we show how to derive the projective superspace solutions from the harmonic superspace solutions.