SUSY in the Sky with Gravitons

TL;DR

This paper reveals a hidden $ ext{N}=2$ supersymmetry in the gravitational scattering of spinning compact bodies, enabling new calculations of deflections and scattering angles in arbitrary dimensions using a supersymmetric worldline quantum field theory approach.

Contribution

It introduces a quadratic-in-spin extension of the worldline quantum field theory incorporating supersymmetry and finite-size effects, advancing the calculation of gravitational scattering observables.

Findings

Derived the deflection and spin kick at sub-leading order in G.

Obtained scattering angles for aligned spins.

Established supersymmetry invariance of the eikonal phase.

Abstract

Picture yourself in the wave zone of a gravitational scattering event of two massive, spinning compact bodies (black holes, neutron stars or stars). We show that this system of genuine astrophysical interest enjoys a hidden $\mathcal{N}=2$ supersymmetry, at least to the order of spin-squared (quadrupole) interactions in arbitrary $D$ spacetime dimensions. Using the ${\mathcal N}=2$ supersymmetric worldline action, augmented by finite-size corrections for the non-Kerr black hole case, we build a quadratic-in-spin extension to the worldline quantum field theory (WQFT) formalism introduced in our previous work, and calculate the two bodies' deflection and spin kick to sub-leading order in the post-Minkowskian expansion in Newton's constant $G$. For spins aligned to the normal vector of the scattering plane we also obtain the scattering angle. All $D$-dimensional observables are derived from an eikonal phase given as the free energy of the WQFT, that is invariant under the $\mathcal{N}=2$ supersymmetry transformations.