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arXiv 2203.07397hep-thmath-phmath.MP
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双场论的规范结构遵循Yang-Mills理论

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

Roberto Bonezzi, Felipe Diaz-Jaramillo, Olaf Hohm

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36 pages, published version
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摘要：

我们证明了到三阶双场论是用杨-米尔斯理论编码的。为此，我们使用弦场论的代数结构如下：杨-米尔斯理论的$L_{\infty}$ -代数是规范群的李代数$\mathfrak{g}$和“运动学代数”${\cal K}$的张量积${\cal K}\otimes \mathfrak{g}$，${\cal K}$是$C_{\infty}$ -代数。这种结构导致了一个三次截断的$L_{\infty}$ -代数上的水平匹配的状态的张量积${\cal K}\otimes \bar{\cal K}$的两个副本的运动学代数的子空间。这个$L_{\infty}$ -代数编码双场论。更确切地说，这种构造依赖于从弦场论或从适当的世界线理论的量子化中得出的杨-米尔斯$L_{\infty}$ -代数的特定形式。

英文摘要：

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.

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