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

TL;DR

This paper develops an off-shell recursion method for gravity and graviton currents within perturbative double field theory, extending the classical double copy concept to off-shell quantities and providing explicit recursive solutions.

Contribution

It introduces the off-shell recursion for gravity and graviton currents in perturbative DFT, and extends the classical double copy to off-shell currents with explicit KLT relations.

Findings

Derived the graviton off-shell recursion using perturbiner method.

Explicitly solved the recursion to obtain graviton off-shell currents.

Extended the classical double copy to off-shell currents with current KLT relations.

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.