SUSY in the sky

TL;DR

This work shows that spinning particles in curved space-time can possess fermionic supersymmetries generated by the square roots of bosonic constants of motion beyond the Hamiltonian. By developing a covariant, pseudo-classical formalism and introducing f-symbols, the authors derive general conditions for new supersymmetries and analyze their Poisson-Dirac algebra, including closure. A key result is the identification of a new non-trivial supersymmetry in Kerr-Newman black-hole backgrounds, realized through the Killing-Yano tensor, with explicit expressions for the associated Killing tensor, vector, and scalar that define the conserved charge Z. The framework links hidden supersymmetries to the separability structures underlying the Dirac equation in curved spacetimes and provides a systematic method to construct and study these symmetries in physically relevant metrics.

Abstract

Spinning particles in curved space-time can have fermionic symmetries generated by the square root of bosonic constants of motion other than the Hamiltonian. We present a general analysis of the conditions under which such new supersymmetries appear, and discuss the Poisson-Dirac algebra of the resulting set of charges, including the conditions of closure of the new algebra. An example of a new non-trivial supersymmetry is found in black-hole solutions of the Kerr-Newman type and corresponds to the Killing-Yano tensor, which plays an important role in solving the Dirac equation in these black-hole metrics.