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.
Highlights
As an alternative theory of gravity, double field theory (DFT) reformulates the closed string low energy effective field theory by requiring the manifest O(D, D) T-duality [5–11]
This paper presents the classical double copy for graviton off-shell currents
We have found the explicit field redefinition between the perturbation of the generalised metric and metric perturbations in GR. This shows the equivalence between perturbative DFT and the perturbative GR
Summary
We construct the perturbation theory of double field theory (DFT) as an alternative tool to the perturbative GR. We first analyse the structure of the perturbation of the generalised metric by solving the O(D, D) constraint exactly. We find the relation between the generalised metric perturbation and the metric perturbation in GR. We construct action and EoM of the perturbative DFT for pure gravity including all-orders in. We discuss the gauge choice of the generalised metric, which is closely related to the de Donder gauge fixing in perturbative GR
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