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 $L_{\infty }$-algebra of Yang-Mills theory is the tensor product $\mathcal{K}\otimes \mathfrak{g}$ of the Lie algebra $\mathfrak{g}$ of the gauge group and a `kinematic algebra' $\mathcal{K}$ that is a $C_{\infty }$-algebra. This structure induces a cubic truncation of an $L_{\infty }$-algebra on the subspace of level-matched states of the tensor product $\mathcal{K}\otimes \bar{\mathcal{K}}$ of two copies of the kinematic algebra. This $L_{\infty }$-algebra encodes double field theory. More precisely, this construction relies on a particular form of the Yang-Mills $L_{\infty }$-algebra following from string field theory or from the quantization of a suitable worldline theory.

arXiv comment36 pages, published version

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