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

TL;DR

This paper demonstrates that double field theory's gauge structure up to cubic order can be derived from Yang-Mills theory using algebraic structures from string field theory, revealing a deep connection between these theories.

Contribution

It shows that the gauge structure of double field theory is encoded in Yang-Mills theory through an $L_{ abla}$-algebra derived from string field theory, establishing a novel algebraic link.

Findings

Double field theory is encoded in Yang-Mills theory at cubic order.

The $L_{ abla}$-algebra structure arises from tensor products of kinematic and gauge Lie algebras.

The construction relies on algebraic structures from string field theory and worldline quantization.

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 ${\cal K}\otimes \mathfrak{g}$ of the Lie algebra $\mathfrak{g}$ of the gauge group and a `kinematic algebra' ${\cal K}$ 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 ${\cal K}\otimes \bar{\cal K}$ 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.