Conservative Black Hole Scattering at Fifth Post-Minkowskian and First Self-Force Order.

We compute the fifth post-Minkowskian (5PM) order contributions to the scattering angle and impulse of classical black hole scattering in the conservative sector at first self-force order using the worldline quantum field theory formalism. This challenging four-loop computation required the use of advanced integration-by-parts and differential equation technology implemented on high-performance computing systems. Use of partial fraction identities allowed us to render the complete integrand in a fully planar form. The resulting function space is simpler than expected: In the scattering angle, we see only multiple polylogarithms up to weight three and a total absence of the elliptic integrals that appeared at 4PM order. All checks on our result, both internal-cancellation of dimensional regularization poles and preservation of the on-shell condition-and external-matching the slow-velocity limit with the post-Newtonian (PN) literature up to 5PN order and matching the tail terms to the 4PM loss of energy-are passed.

Conservative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order.

Using the N=1 supersymmetric, spinning worldline quantum field theory formalism, we compute the conservative spin-orbit part of the momentum impulse Δp_{i}^{µ}, spin kick ΔS_{i}^{µ}, and scattering angle θ from the scattering of two spinning massive bodies (black holes or neutron stars) up to fourth post-Minkowskian (PM) order. These three-loop results extend the state of the art for generically spinning binaries from 3PM to 4PM. They are obtained by employing recursion relations for the integrand construction and advanced multiloop Feynman integral technology in the causal (in-in) worldline quantum field theory framework to directly produce classical observables. We focus on the conservative contribution (including tail effects) and outline the computations for the dissipative contributions as well. Our spin-orbit results agree with next-to-next-to-next-to-leading-order post-Newtonian and test-body data in the respective limits. We also reconfirm the conservative 4PM nonspinning results.

Dissipative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order.

We compute the radiation reacted momentum impulse Δp_{i}^{µ}, spin kick ΔS_{i}^{µ}, and scattering angle θ between two scattered spinning massive bodies (black holes or neutron stars) using the N=1 supersymmetric worldline quantum field theory formalism up to fourth post-Minkowskian (4PM) order. Our calculation confirms the state-of-the-art nonspinning results, and extends them to include spin-orbit effects. Advanced multiloop Feynman integral technology including differential equations and the method of regions are applied and extended to deal with the retarded propagators arising in a causal description of the scattering dynamics. From these results we determine a complete set of radiative fluxes at subleading PM order: the 4PM radiated four-momentum and, via linear response, the 3PM radiated angular momentum, both again including spin-orbit effects.

Conservative and Radiative Dynamics of Spinning Bodies at Third Post-Minkowskian Order Using Worldline Quantum Field Theory.

Using the spinning worldline quantum field theory formalism we calculate the quadratic-in-spin momentum impulse Δp_{i}^{µ} and spin kick Δa_{i}^{µ} from a scattering of two arbitrarily oriented spinning massive bodies (black holes or neutron stars) in a weak gravitational background up to third post-Minkowskian (PM) order (G^{3}). Two-loop Feynman integrals are performed in the potential region, yielding conservative results. For spins aligned to the orbital angular momentum we find a conservative scattering angle that is fully consistent with state-of-the-art post-Newtonian results. Using the 2PM radiated angular momentum previously obtained by Plefka, Steinhoff, and the present authors, we generalize the angle to include radiation-reaction effects, in which case it avoids divergences in the high-energy limit.

Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies.

The recently established formalism of a worldline quantum field theory, which describes the classical scattering of massive bodies (black holes, neutron stars, or stars) in Einstein gravity, is generalized up to quadratic order in spin, revealing an alternative N=2 supersymmetric description of the symmetries inherent in spinning bodies. The far-field time domain waveform of the gravitational waves produced in such a spinning encounter is computed at leading order in the post-Minkowskian (weak field, but generic velocity) expansion, and exhibits this supersymmetry. From the waveform we extract the leading-order total radiated angular momentum in a generic reference frame, and the total radiated energy in the center-of-mass frame to leading order in a low-velocity approximation.

Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory.

Using the recently established formalism of a worldline quantum field theory description of the classical scattering of two spinless black holes, we compute the far-field time-domain waveform of the gravitational waves produced in the encounter at leading order in the post-Minkowskian (weak field but generic velocity) expansion. We reproduce the previous results of Kovacs and Thorne in a highly economic way. Then, using the waveform, we extract the leading-order total radiated angular momentum and energy (including differential results). Our work may enable crucial improvements of gravitational-wave predictions in the regime of large relative velocities.

Full-Color Two-Loop Four-Gluon Amplitude in N=2 Supersymmetric QCD.

We present the fully integrated form of the two-loop four-gluon amplitude in N=2 supersymmetric quantum chromodynamics with gauge group SU(N_{c}) and with N_{f} massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on N_{c} and N_{f}, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the N=2 superconformal theory, where N_{f}=2N_{c}, we obtain remarkably simple amplitudes that have an analytic structure close to that of N=4 super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.