Abstract
We construct the classical double copy formalism for M-theory. This extends the current state of the art by including the three form potential of eleven dimensional supergravity along with the metric. The key for this extension is to construct a Kerr-Schild type Ansatz for exceptional field theory. This Kerr-Schild Ansatz then allows us to find the solutions of charged objects such as the membrane from a set of single copy fields. The exceptional field theory formalism then automatically produces the IIB Kerr-Schild ansatz allowing the construction of the single copy for the fields of IIB supergravity (with manifest SL(2) symmetry).
Highlights
A central component in the construction of the classical double copy has been the use of the Kerr-Schild Ansatz
First we will construct a universal Kerr-Schild ansatz. This is an ansatz that will be valid for GR, DFT or Exceptional field theory that will reduce the theory to a set of linear equations
We show that solutions of the exceptional field theory with the Kerr-Schild Ansatz are given by a Maxwell field and a two form potential obeying their respective linear equations of motion. (In Exceptional Field Theory (ExFT) language, the single copy field of the SL(5) exceptional field theory is a vector in the 10 of SL(5))
Summary
We will consider the Kerr-Schild (KS) ansatz for General Relativity, Double. Even though each theory has different properties (for example their actions are different), we are able to write a universal Kerr-Schild ansatz in terms of a null (generalised) vector and a projection operator which is defined for each theory. Note, that this does not mean that all solutions of general relativity or eleven dimensional supergravity are secretly linear. To maintain the consistency of the theory we must only consider fluctuations δMMN that preserve the coset structure of the metric (even off shell) This is done by introducing a projection operator PMN P Q so that perturbations of the generalised metric δMMN satisfy [102, 103]. In the following we will review the known examples, GR and DFT, and introduce the KS ansatz for SL(5) ExFT
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