Heterotic Kerr-Schild Double Field Theory and Classical Double Copy

Abstract

We discuss the generalization of the Kerr-Schild (KS) formalism for general relativity and double field theory (DFT) to the heterotic DFT and supergravity. We first introduce a heterotic KS ansatz by introducing a pair of null O(d,d+G) generalized tangent vectors. The pair of null vectors are represented by a pair of d-dimensional vector fields, and one of the vector fields is not a null vector. This implies that the null property of the usual KS formalism, which plays a crucial role in linearizing the field equations, can be partially relaxed in a consistent way. We show that the equations of motion under the heterotic KS ansatz in a flat background can be reduced to linear equations. Using the heterotic KS equations, we establish the single and zeroth copy for heterotic supergravity and derive the Maxwell and Maxwell-scalar equations. This agrees with the KLT relation for heterotic string theory.

30 pages; typos corrected

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• The classical double copy of non-singular black holes
• The Classical Double Copy of a Point Charge
• Classical Yang-Mills observables from amplitudes
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• Weyl doubling
• New heavenly double copies
• Asymptotic Weyl Double Copy
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Einstein-Maxwell theory and the Weyl double copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Twistor Space Origins of the Newman-Penrose Map
• On the Lagrangian formulation of the double copy to cubic order
• Isometries and the double copy
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
• $\mathcal{N}=1$ Supersymmetric Double Field Theory and the generalized Kerr-Schild Ansatz
• Higher-derivative Heterotic Double Field Theory and Classical Double Copy
• Generalized Black Holes in 3D Kerr-Schild Double Copy
• The Classical Double Copy for Half-Maximal Supergravities and T-duality
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Beyond the standard model with six-dimensional spinors
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Note on the asymptotic structure of Kerr-Schild form
• Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation
• Compactifying the Kerr-Schild Double Copy
• The Weyl double copy from twistor space
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• NS-NS Spacetimes from Amplitudes
• Kerr-Schild Double Copy of the Randall-Sundrum Black String