论文标题
双场理论的仪表结构遵循杨米尔斯理论
The Gauge Structure of Double Field Theory follows from Yang-Mills Theory
论文作者
论文摘要
我们表明，对于立方顺序，双场理论是在杨米尔斯理论中编码的。为此，我们使用字符串字段理论的代数结构如下：yang-mills理论的$ l _ {\ infty} $ - 代数是tensor产品$ {\ cal k} \ otimes \ otimes \ mathfrak {g mathfrak {g} $ {\ cal k} $是$ c _ {\ infty} $ - 代数。这种结构引起了$ l _ {\ infty} $ - 代数的立方截断，该代数是张量产品$ {\ cal k} \ otimes \ otimes \ bar {\ cal k} $ space的子空间的，这是Kinematic Algebra的两个副本。这个$ l _ {\ infty} $ - 代数编码双字段理论。更确切地说，这种构建依赖于Yang-Mills $ L _ {\ Infty} $ - 符合字符串字段理论的代数或合适的世界线理论的特定形式。
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.
