arXiv subjects

Nabha Shah

Publications and source records attributed to Nabha Shah.

9 recordsLinked to original sources

arXiv2026

The gravitational Compton amplitude at third post-Minkowskian order

We employ a single worldline effective field theory in a Schwarzschild--Tangherlini background to compute the gravitational Compton amplitude up to third post-Minkowskian order. By exposing the structure of infrared and forward divergences of the post-Minkowskian expansion, we are able to regulate these divergences, thereby establishing an exact and useful computational bridge to results in black hole perturbation theory. We also outline possible applications for Compton amplitudes with finite-size effects, such as spin and tidal features.

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arXiv2025

The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order

We utilize various computational techniques in flat and curved backgrounds to calculate the classical gravitational Compton amplitude up to the second post-Minkowskian order. Our novel result supports the use of worldline quantum field theory in non-trivial background spacetimes to obtain new theoretical insights that can both enhance computational efficiency and provide useful cross-checks of results, particularly in the context of classical binary black hole mergers.

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arXiv2024

Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory

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.

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arXiv2024

Effective Field Theory for Extreme Mass Ratios

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.

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arXiv2024

Generalized Symmetry in Dynamical Gravity

We explore generalized symmetry in the context of nonlinear dynamical gravity. Our basic strategy is to transcribe known results from Yang-Mills theory directly to gravity via the tetrad formalism, which recasts general relativity as a gauge theory of the local Lorentz group. By analogy, we deduce that gravity exhibits a one-form symmetry implemented by an operator $U_α$ labeled by a center element $α$ of the Lorentz group and associated with a certain area measured in Planck units. The corresponding charged line operator $W_ρ$ is the holonomy in a spin representation $ρ$, which is the gravitational analog of a Wilson loop. The topological linking of $U_α$ and $W_ρ$ has an elegant physical interpretation from classical gravitation: the former materializes an exotic chiral cosmic string defect whose quantized conical deficit angle is measured by the latter. We verify this claim explicitly in an AdS-Schwarzschild black hole background. Notably, our conclusions imply that the standard model exhibits a new symmetry of nature at scales below the lightest neutrino mass. More generally, the absence of global symmetries in quantum gravity suggests that the gravitational one-form symmetry is either gauged or explicitly broken. The latter mandates the existence of fermions. Finally, we comment on generalizations to magnetic higher-form or higher-group gravitational symmetries.

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arXiv2022

Non-perturbative Double Copy in Flatland

We derive a non-perturbative, 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 non-perturbative 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.

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arXiv2020

Mining the Geodesic Equation for Scattering Data

The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the presence of perturbatively small effects such as tidal distortion and higher derivative corrections to general relativity. We derive an algebraic map between the perturbed geodesic equation and the leading PM scattering amplitude at arbitrary mass ratio. As examples, we compute formulas for amplitudes and isotropic gauge Hamiltonians for certain infinite classes of tidal operators such as electric or magnetic Weyl to any power, and for higher derivative corrections to gravitationally interacting bodies with or without electric charge. Finally, we present a general method for calculating closed-form expressions for amplitudes and isotropic gauge Hamiltonians in the test-particle limit at all orders in the PM expansion.

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arXiv2017

Deriving spin-1 quartic interaction vertices from closure of the Poincaré algebra

We derive the quartic interaction vertex of pure Yang-Mills theory by demanding closure of the light-cone Poincaré algebra in four-dimensional Minkowski spacetime. This calculation explicitly shows why structure constants must satisfy the Jacobi identity. We then prove that corrections to the spin generator, for spin one at this order, vanish. We comment briefly on higher spin fields in this context.

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arXiv2017

Gravitation and quadratic forms

The light-cone Hamiltonians describing both pure Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

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