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.

Snowmass White Paper: the Double Copy and its Applications

“…Explicit color-dual solutions have found an off-shell realization through classical perturbiner solutions [131][132][133] in so-called BCJ gauge [141,142,144]. Just this year there has additionally been new insight into double-copying off shell currents [552] and the kinematic algebra [553] from the perspective of double-field theory.…”

The SAGEX Review on Scattering Amplitudes, Chapter 14: Classical Gravity from Scattering Amplitudes

“…Ref. [231] showed that currents (one leg off-shell) obtained from perturbative double field theory satisfy a simple generalisation of the on-shell KLT relations; see [232,233] for related work. Regarding complete 'off-shellness', it is worth mentioning that there exist elegant and useful Lagrangians for gravity that were at least motivated by the double copy [234,235].…”

The Gauge Structure of Double Field Theory follows from Yang-Mills Theory

“…Recently, together with Plefka, two of us established in [13] a close double copy relation to cubic order between the Lagrangians of Yang-Mills theory and double field theory (DFT) [14][15][16][17][18], which is a formulation of the string target space theory for graviton, B-field and dilaton that is T-duality invariant thanks to doubled coordinates. (See [19][20][21][22][23][24] for reviews and earlier work and [25][26][27] for previous work on double copy and DFT.) The construction of [13] requires integrating out the DFT dilaton and picking Siegel gauge at cubic order.…”