We explore a recently proposed effective field theory describing electromagnetically or gravitationally interacting massive particles in an expansion about their mass ratio, also known as the self-force (SF) expansion. By integrating out the deviation of the heavy particle about its inertial trajectory, we obtain an effective action whose only degrees of freedom are the lighter particle together with the photon or graviton, all propagating in a Coulomb or Schwarzschild background. The 0SF dynamics are described by the usual background field method, which at 1SF is supplemented by a “recoil operator” that encodes the wobble of the heavy particle, and similarly computable corrections appearing at 2SF and higher. Our formalism exploits the fact that the analytic expressions for classical backgrounds and particle trajectories encode dynamical information to all orders in the couplings, and from them we extract multiloop integrands for perturbative scattering. As a check, we study the two-loop classical scattering of scalar particles in electromagnetism and gravity, verifying known results. We then present new calculations for the two-loop classical scattering of dyons, and of particles interacting with an additional scalar or vector field coupling directly to the lighter particle but only gravitationally to the heavier particle.

United States

Clifford Cheung

France

Julio Parra-Martinez

Ira Rothstein

Nabha Shah

Jordan Wilson-Gerow

Gravitational scattering and beyond from extreme mass ratio effective field theory

We derive a soft theorem for a massless scalar in an effective field theory with generic field content using the geometry of field space. This result extends the geometric soft theorem for scalar effective field theories by allowing the massless scalar to couple to other scalars, fermions, and gauge bosons. The soft theorem keeps its geometric form, but where the field-space geometry now involves the full field content of the theory. As a bonus, we also present novel double soft theorems with fermions, which mimic the geometric structure of the double soft theorem for scalars.

Maria Derda

CERN

Andreas Helset

Canada

Soft scalars in effective field theory

We present a framework to compute amplitudes for the gravitational analog of the Raman process, a quasielastic scattering of waves off compact objects, in worldline effective field theory. As an example, we calculate third post-Minkowskian order [<math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>3</mn></msup><mo>)</mo></math>], or two-loop, phase shifts for the scattering of a massless scalar field including all tidal effects and dissipation. Our calculation unveils two sources of the classical renormalization-group flow of dynamical Love numbers: a universal running independent of the nature of the compact object, and a running self-induced by tides. Restricting to the black hole case, we find that our effective field theory phase shifts agree exactly with those from general relativity, provided that the relevant static Love numbers are set to zero. In addition, we carry out a complete matching of the leading scalar dynamical Love number required to renormalize a universal short scale divergence in the <math><mi>S</mi></math> wave. Our results pave the way for systematic calculations of gravitational Raman scattering at higher post-Minkowskian orders.

Mikhail M. Ivanov

Yue-Zhou Li

Zihan Zhou

Gravitational Raman Scattering in Effective Field Theory: A Scalar Tidal Matching at <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>3</mn></msup><mo>)</mo></math>

We derive an effective field theory describing a pair of gravitationally interacting point particles in an expansion in their mass ratio, also known as the self-force (SF) expansion. The 0SF dynamics are trivially obtained to all orders in Newton’s constant by the geodesic motion of the light body in a Schwarzschild background encoding the gravitational field of the heavy body. The corrections at 1SF and higher are generated by perturbations about this configuration—that is, the geodesic deviation of the light body and the fluctuation graviton—but crucially supplemented by an operator describing the recoil of the heavy body as it interacts with the smaller companion. Using this formalism we compute new results at third post-Minkowskian order for the conservative dynamics of a system of gravitationally interacting massive particles coupled to a set of additional scalar and vector fields.

Ira Z. Rothstein

Effective Field Theory for Extreme Mass Ratio Binaries

A variety of condensed matter systems describe gapless modes that can be interpreted as Nambu-Goldstone bosons of spontaneously broken Poincaré symmetry. In this paper we derive new soft theorems constraining the tree-level scattering of these degrees of freedom, as exhibited in solids, fluids, superfluids, and framids. These soft theorems are in one-to-one correspondence with various broken symmetries, including spacetime translations, Lorentz boosts, and, for the case of fluids, volume-preserving diffeomorphisms. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories.

Soft phonon theorems

Do gravitational interactions respect the basic principles of relativity and quantum mechanics? We show that any graviton <math><mi>S</mi></math>-matrix that satisfies these assumptions cannot significantly differ from General Relativity at low energies. We provide sharp bounds on the size of potential corrections in terms of the mass <math><mi>M</mi></math> of new higher-spin states, in spacetime dimensions <math><mi>D</mi><mo>≥</mo><mn>5</mn></math> where the <math><mi>S</mi></math>-matrix does not suffer from infrared ambiguities. The key novel ingredient is the full set of <math><mrow><mi>SO</mi><mo>(</mo><mi>D</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math> partial waves for this process, which we show how to efficiently compute with Young tableau manipulations. We record new bounds on the central charges of holographic conformal theories.

Simon Caron-Huot

David Simmons-Duffin

Graviton partial waves and causality in higher dimensions

We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a pointlike particle carrying a scalar charge <math><mi>Q</mi></math> off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full <math><mi>O</mi><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> scalar-field self-force term (but ignoring the gravitational self-force), and we compare with analytical expressions obtained in a PM framework using scattering-amplitude methods. This example provides a nontrivial, high-precision test of both calculation methods and illustrates the complementarity of the two approaches in the context of the program to provide high-precision models of gravitational two-body dynamics. Our PM calculation is carried out through 4PM order, i.e., including all terms through <math><mi>O</mi><mo>(</mo><msup><mi>Q</mi><mn>2</mn></msup><msup><mi>G</mi><mn>3</mn></msup><mo>)</mo></math>. At the fourth post-Minkowskian order the point-particle description involves two a priori undetermined coefficients, due to contributions from tidal effects in the model under consideration. These coefficients are chosen to align the post-Minkowskian results with the self-force ones.

United Kingdom

Leor Barack

Zvi Bern

Enrico Herrmann

Germany

Oliver Long

Radu Roiban

Michael S. Ruf

Chia-Hsien Shen

Mikhail P. Solon

Fei Teng

Mao Zeng

Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model

We study constraints from causality and unitarity on 2 → 2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G → 0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.

Causality constraints on corrections to Einstein gravity

We derive a nonperturbative, Lagrangian-level formulation of the double copy in two spacetime dimensions. Our results elucidate the field theoretic underpinnings of the double copy in a broad class of scalar theories which can include masses and higher-dimension operators. An immediate corollary is the amplitudes-level double copy at all orders in perturbation theory. Applied to certain integrable models, the double copy defines an isomorphism between Lax connections, Wilson lines, and infinite towers of conserved currents. We also implement the double copy at the level of nonperturbative classical solutions, both analytically and numerically, and present a generalization of the double copy map that includes a fixed tower of higher-dimension corrections given by the Moyal algebra.

James Mangan

Nonperturbative Double Copy in Flatland

We propose a mapping between geometry and kinematics that implies the classical equivalence of any theory of massless bosons—including spin and exhibiting arbitrary derivative or potential interactions—to a nonlinear sigma model (NLSM) with a momentum-dependent metric in field space. From this kinematic metric we construct a corresponding kinematic connection, covariant derivative, and curvature, all of which transform appropriately under general field redefinitions, even including derivatives. We show explicitly how all tree-level on-shell scattering amplitudes of massless bosons are equal to those of the NLSM via the replacement of geometry with kinematics. Lastly, we describe how the recently introduced geometric soft theorem of the NLSM, which universally encodes all leading and subleading soft scalar theorems, also captures the soft photon theorems.

Geometry-kinematics duality