The off-shell recursion for gravity and the classical double copy for currents

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.

Automated summary

The paper introduces a novel off-shell recursion and graviton current for gravity in perturbative double field theory. By utilizing the perturbiner method, the graviton off-shell recursion is derived from the equations of motion for perturbative DFT, leading to explicit graviton off-shell currents. The classical double copy and KLT relation for gravity are discussed with insights into off-shell conservation of currents for nonlinear gauge choices.