The Gauge Structure of Double Field Theory follows from Yang-Mills Theory

Abstract

We show that to cubic order double field theory is encoded in Yang-Mills theory. To this end we use algebraic structures from string field theory as follows: The L ∞ -algebra of Yang-Mills theory is the tensor product K ⊗ g of the Lie algebra g of the gauge group and a 'kinematic algebra' K that is a C ∞ -algebra. This structure induces a cubic truncation of an L ∞ -algebra on the subspace of level-matched states of the tensor product K⊗ K of two copies of the kinematic algebra. This L ∞ -algebra encodes double field theory. More precisely, this construction relies on a particular form of the Yang-Mills L ∞ -algebra following from string field theory or from the quantization of a suitable worldline theory.

The SAGEX review on scattering amplitudes Chapter 14: Classical gravity from scattering amplitudes

“…Reference [246] described a 'covariant colour-kinematics duality' at the level of the equations of motion. Reference [247] showed that currents (one leg off-shell) obtained from perturbative DFT satisfy a simple generalisation of the on-shell KLT relations; see [248][249][250] for related work. Regarding complete 'off-shellness', it is worth mentioning that there exist elegant and useful Lagrangians for gravity that were at least motivated by the double copy [251,252].…”