Self-duality and supersymmetry

Understand

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.