The Off-Shell Recursion for Gravity and the Classical Double Copy for currents

Abstract

We construct the off-shell recursion for gravity and the graviton current for the perturbative double field theory (DFT). We first formulate the perturbative DFT, which is equivalent but simpler to perturbative general relativity, to all-orders in fluctuations of generalised metric. The perturbative action and equations of motion (EoM) are derived to arbitrary order for pure gravity case. We then derive the graviton off-shell recursion, the gravity counterpart of the Berends-Giele recursion in Yang-Mills theory, through the so-called perturbiner method using the EoM of the perturbative DFT. We solve the recursion iteratively and obtain the graviton off-shell currents explicitly. We then discuss the classical double copy for the off-shell currents. We present the current KLT relation for gravity by extending the result proposed by Mizera and Skrzypek for the non-gravitational effective field theories. The relation represents graviton currents by squaring gluon currents with the KLT kernel up to gauge transformation and regular terms that do not have any pole. Finally we discuss the off-shell conservation of currents for nonlinear gauge choices.

38 pages; v2: minor changes and fixes; v3: references added, published version

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• One-loop off-shell amplitudes from classical equations of motion
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Note on the asymptotic structure of Kerr-Schild form
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• Berends-Giele currents for extended gravity
• One-loop $N$-point correlators in pure gravity
• Massive strings from a haunted field theory
• Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
• The off-shell expansion relation of the Yang-Mills scalar theory
• Quantum Off-Shell Recursion Relation
• Cotton Double Copy for Gravitational Waves
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