The classical double copy for half-maximal supergravities and T-duality. (English) Zbl 1476.83167
Summary: 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.
MSC:
| 83E50 | Supergravity |
| 83C57 | Black holes |
| 83E15 | Kaluza-Klein and other higher-dimensional theories |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
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