The classical double copy for half-maximal supergravities and T-duality

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.

The off-shell recursion for gravity and the classical double copy for currents

“…The double copy is a relation between gravity and the Yang-Mills theory, which originated in graviton scattering, and it defines a map between graviton and gluon amplitudes [19][20][21][22][23][24][25][26][27][28][29][30]. It turns out that DFT and the double copy share the common origin from the closed string theory, in particular the factorisation into left-and right-moving sectors [31][32][33][34][35][36][37][38][39]. The double copy prescription has recently been extended to solutions of the classical equations of motion (EoM), the so-called classical double copy [34,[40][41][42], by establishing the map between the gravity and gauge theory solutions [36,.…”

The SAGEX Review on Scattering Amplitudes, Chapter 14: Classical Gravity from Scattering Amplitudes

“…[197], a Kerr-Schild-type ansatz in heterotic DFT provided examples of exact double copy, an idea further developed in refs. [198][199][200][201]. Extensions to exceptional field theories, which arise in the low-energy limit of string/M-theory, were presented in refs.…”

Heterotic Kerr-Schild Double Field Theory and its double Yang-Mills formulation

“…The GKSA was originally formulated in [8] and it has been explored in heterotic DFT [9] [22] [23], Kaluza-Klein DFT [24], Exceptional Field Theory [25], among others [16] [26].…”