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

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