The gauge structure of double field theory follows from Yang-Mills theory

A Minimal b Ghost

“…The algebraic behaviour of b are essential for proving properties of amplitudes like color‐kinematics duality and double copy. [ 21,30–32 ] Its failure to be a derivation defines the brackets for the kinetic Lie algebra. We have not examined this in detail for $$b^{\prime }$$.…”

Gravity = Yang–Mills

“…One may then define the larger class of Yang-Mills-type theories as the tensor product of K with more general 'Lie-type' algebras, namely homotopy Lie or L 8 algebras. The kinematic algebra K itself carries, in a hidden way, such a Lie-type algebra up to obstructions that, however, cancel on a subspace of the tensor product K b K with a second copy K, as has been proved to the order relevant for quartic couplings [8][9][10]. We may thus define the yet larger class of Yang-Mills-type theories as those given by the tensor product of K with an obstructed Lie-type algebra for which the obstructions are canceled on a non-trivial subspace.…”

“…(An operator b and an associated BV 8 algebra are also realized in self-dual Yang-Mills theory [22] and 3D Chern-Simons theory [8,23,24]. )…”

Radiative phase space extensions at all orders in r for self-dual Yang-Mills and gravity

“…In the search for a more general double copy map, a valuable criterion is the robustness under local transformations, i.e. the requirement that diffeomorphism transformations in gravity follow from gauge transformations in YM [34][35][36][37][38][39][40][41][42][43][44][45]. In [24] one of the authors constructed the first non-perturbative such map for a subset of the local symmetries, looking at infinitessimal transformations.…”