Self-duality and supersymmetry

TL;DR

This paper explores the supersymmetric properties of Hamiltonians derived from the 4d Dirac operator in self-dual backgrounds, extending to curved manifolds and connecting with harmonic superspace formulations.

Contribution

It demonstrates the supersymmetry of the Hamiltonian in self-dual backgrounds and generalizes the model to curved conformally flat 4d manifolds.

Findings

Hamiltonian H = D^2 is supersymmetric with 4 supercharges.

Extension of the model to curved conformally flat 4d manifolds.

Connection to harmonic superspace expressions for Abelian backgrounds.

Abstract

We observe that the Hamiltonian H = D^2, where D is the flat 4d Dirac operator in a self-dual gauge background, is supersymmetric, admitting 4 different real supercharges. A generalization of this model to the motion on a curved conformally flat 4d manifold exists. For an Abelian self-dual background, the corresponding Lagrangian can be derived from known harmonic superspace expressions.