Classical Double Copy of Spinning Worldline Quantum Field Theory

Abstract

We study the classical double copy of massive spinning objects in the worldline quantum field theories (WQFT) formalism. We couple the $\mathcal{N}=1$ supersymmetric model to a Yang-Mills background to describe the propagation of a spin-half particle interacting with gluons. At the classical level, this model captures physical effects up to linear order in spin. We propose a double copy relation to map the spin tensors to the gravitation side. Enforcing R-symmetry and supersymmetry (SUSY) on the double copy integrands, we find that the gravitational theory is the $\mathcal{N}=2$ particle coupled to dilaton-gravity (DG). We check the double copy prescription for the eikonal phase up to next-to-leading order and for radiation at leading order in coupling constants, finding that the Grassmann nature of the spin tensor in WQFT plays a crucial role in finding full agreement with direct calculation in the $\mathcal{N}=2$ model. We show how to deform the SUSY charges of the free theory to include DG. Since the constraints algebra is first class, the worldline model can be quantized, describing the propagation of a massive vector field coupled to DG, in agreement with the literature. In addition, we investigate the double copy without preserving SUSY and R-symmetry, finding that the B-field also couples to the~worldline.

arXiv comment41 pages, 4 figures

References in corpus (59)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Black holes and the double copy
• The Kinematic Algebra From the Self-Dual Sector
• Radiation and the classical double copy for color charges
• The classical double copy for Taub-NUT spacetime
• Classical black hole scattering from a worldline quantum field theory
• Observables and amplitudes for spinning particles and black holes
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Black-hole scattering with general spin directions from minimal-coupling amplitudes
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Perturbative spacetimes from Yang-Mills theory
• The double copy: Bremsstrahlung and accelerating black holes
• Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering
• Color-Kinematics Duality for QCD Amplitudes
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Double copy for massive quantum particles with spin
• Gravitational Radiation from Color-Kinematics Duality
• Type D Spacetimes and the Weyl Double Copy
• SUSY in the Sky with Gravitons
• Spinning particles, axion radiation, and the classical double copy
• Bound states and the classical double copy
• Gravity as Gauge Theory Squared: A Ghost Story
• A Twistorial Foundation for the Classical Double Copy
• Effective action of dilaton gravity as the classical double copy of Yang-Mills theory
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• Trace Anomalies from Quantum Mechanics
• Worldline approach to vector and antisymmetric tensor fields
• The Weyl Double Copy for Gravitational Waves
• Classical Solutions and their Double Copy in Split Signature
• The Classical Double Copy of a Point Charge
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• Gravitational radiation from the classical spinning double copy
• On the Double Copy for Spinning Matter
• Classical Double Copy of Worldline Quantum Field Theory
• Gauge and Gravity Amplitude Relations
• Worldgraph Approach to Yang-Mills Amplitudes from N=2 Spinning Particle
• Worldline approach to vector and antisymmetric tensor fields II
• Helicity amplitudes for QCD with massive quarks
• Strings, extended objects, and the classical double copy
• The Double Copy of Massive Scalar-QCD
• The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Dressed scalar propagator in a non-abelian background from the worldline formalism
• The double copy of the multipole expansion
• Einstein gravity from the $\mathbb{N}=4$ spinning particle
• Geodesics From Classical Double Copy
• A Worldline Theory for Supergravity
• Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes
• Classical off-shell currents
• One-loop quantum gravity from the N=4 spinning particle
• Worldline description of a bi-adjoint scalar and the zeroth copy
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• Classical gravitational scattering from a gauge-invariant double copy

Cited by in corpus (6)

• Inelastic Exponentiation and Classical Gravitational Scattering at One Loop
• Recursion in the classical limit and the neutron-star Compton amplitude
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Loop-level double-copy for massive fermions in the fundamental
• Ab Initio Construction of Poincaré and AdS Particle