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.

41 pages, 4 figures

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• New Relations for Gauge-Theory Amplitudes
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• Loop-level double-copy for massive fermions in the fundamental
• Ab Initio Construction of Poincaré and AdS Particle