The Classical Double Copy for Half-Maximal Supergravities and T-duality

TL;DR

This paper extends the classical double copy framework to half-maximal supergravities via Kaluza-Klein reduction of double field theory, revealing new insights into T-duality transformations and their effects on solutions.

Contribution

It provides a general formula for KK reduction of the DFT Kerr-Schild ansatz and demonstrates that half-maximal supergravities admit a classical double copy structure.

Findings

The KK reduction of the Kerr-Schild ansatz leads to linear equations of motion.

Half-maximal supergravities' single copy is a pair of Maxwell-scalar theories.

T-duality transformations produce new solutions with nontrivial fields.

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.