SUSY in the sky with gravitons

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 $$ \mathcal{N} $$ N = 2 supersymmetry, at least to the order of spin-squared (quadrupole) interactions in arbitrary D spacetime dimensions. Using the $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 2 supersymmetry transformations.

Light bending from eikonal in worldline quantum field theory

“…Indeed, in ref. [17] this model has been used to describe spinning black holes. However, the approach we have used here is closer to the standard QFT setup.…”

“…WQFT shares some similarities with the Effective Field Theory (EFT) approach to gravitational dynamics [12][13][14] with the important difference that in WQFT worldline degrees of freedom are also quantized. The WQFT formalism has been further developed to describe Bremsstrahlung [15], spinning black holes [16,17] and colored massive particles [18].…”

“…The treatment of classical spinning massive particles in WQFT has been discussed at length in ref. [17] so we will build on these results. For the spinning case we will conform ourselves with a LO calculation up to quadratic order in spin.…”

“…The description in ref. [17] is based on the inclusion of supersymmetry at the level of the worldline action.…”

“…After some algebra we compute in agreement with the massless limit of the Kerr-result of ref. [17] (see also refs. [68,69]).…”