Abstract
We study the classical double copy for ungauged half-maximal supergravities using the Kaluza-Klein reduction of double field theory (DFT). We construct a general formula for the Kaluza-Klein (KK) reduction of the DFT Kerr-Schild ansatz. The KK reduction of the ansatz is highly nonlinear, but the associated equations of motion are linear. This linear structure implies that half-maximal supergravities admit a classical double copy. We show that their single copy is given by a pair of Maxwell-scalar theories, which are the KK reduction of a higher-dimensional single copy of DFT. We also investigate their T-duality transformations — both the Buscher rule and continuous O(D, D) rotations. Applying the Buscher rule to the Kerr BH, we obtain a solution with a nontrivial Kalb-Ramond field and dilaton. We also identify the single copy of Sen’s heterotic BH and the chiral null model and show that the chiral null model is self-dual under T-duality rotations.
Highlights
In recent years there has been substantial progress in extending the double copy prescription to exact solutions of the classical equations of motion
We study the classical double copy for ungauged half-maximal supergravities using the Kaluza-Klein reduction of double field theory (DFT)
The KK reduction of the ansatz is highly nonlinear, but the associated equations of motion are linear. This linear structure implies that half-maximal supergravities admit a classical double copy. We show that their single copy is given by a pair of Maxwell-scalar theories, which are the KK reduction of a higher-dimensional single copy of DFT
Summary
Ungauged half-maximal supergravities can be constructed via the Kaluza-Klein reduction of ten-dimensional NSNS supergravity (with or without vector multiplets). If there are n additional vector multiplets, the ten-dimensional supergravity can be embedded into O(10, 10 + n) heterotic DFT. Throughout this paper, we will ignore vector multiplets for simplicity. Since the structure of the bosonic sector of DFT is independent of the spacetime dimension, for generality we will consider O(D, D) DFT. We review the Kaluza-Klein (KK) reduction of DFT and NSNS supergravity and fix our notation. We investigate the KK reduction of the Kerr-Schild (KS) ansatz of DFT. We discuss the KK reduction of the KS equations of motion and show that these remain linear, even though the lower-dimensional KS ansatz is nonlinear even at the level of DFT
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