Radiated Angular Momentum and Dissipative Effects in Classical Scattering.

We present a new formula for the angular momentum J^{μν} carried away by gravitational radiation in classical scattering. This formula, combined with the known expression for the radiated linear momentum P^{μ}, completes the set of radiated Poincaré charges due to scattering. We parametrize P^{μ} and J^{μν} by nonperturbative form factors and derive exact relations using the Poincaré algebra.

Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G^{4}).

We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G^{4}) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity.

Scattering Amplitudes and Conservative Binary Dynamics at O(G^{4}).

Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G^{4}). As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals.

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order.

We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. Adapting methods for integration and matching from effective field theory, we extract the conservative Hamiltonian for compact spinless binaries at third post-Minkowskian order.

Dual Conformal Structure Beyond the Planar Limit.

The planar scattering amplitudes of N=4 super-Yang-Mills theory display symmetries and structures which underlie their relatively simple analytic properties such as having only logarithmic singularities and no poles at infinity. Recent work shows in various nontrivial examples that the simple analytic properties of the planar sector survive into the nonplanar sector, but this has yet to be understood from underlying symmetries. Here, we explicitly show that for an infinite class of nonplanar integrals that covers all subleading-color contributions to the two-loop four- and five-point amplitudes of N=4 super-Yang-Mills theory, symmetries analogous to dual conformal invariance exist.

Vector Effective Field Theories from Soft Limits.

We present a bottom-up construction of vector effective field theories using the infrared structure of scattering amplitudes. Our results employ two distinct probes of soft kinematics: multiple soft limits and single soft limits after dimensional reduction applicable in four and general dimensions, respectively. Both approaches uniquely specify the Born-Infeld (BI) model as the only theory of vectors completely fixed by certain infrared conditions which generalize the Adler zero for pions.

Symmetry for Flavor-Kinematics Duality from an Action.

We propose a new representation of the nonlinear sigma model that exhibits a manifest duality between flavor and kinematics. The fields couple exclusively through cubic Feynman vertices which define the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities.

On-Shell Recursion Relations for Effective Field Theories.

We derive the first ever on-shell recursion relations applicable to effective field theories. Based solely on factorization and the soft behavior of amplitudes, these recursion relations employ a new rescaling momentum shift to construct all tree-level scattering amplitudes in the nonlinear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results prove that all theories with enhanced soft behavior are on-shell constructible.

Nonrenormalization Theorems without Supersymmetry.

We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations.