论文标题
$ l _ {\ infty} $具有物质的仪表理论的结构
The $L_{\infty}$ structure of gauge theories with matter
论文作者
论文摘要
在这项工作中，我们提出了一种代数方法，以实现对物质耦合的量表理论的动力学和扰动理论。我们要考虑的现场理论是：Chern-Simons-Marts，量子染色体动力学和标量量子染色体动力学。从经典的Batalin-Vilkovisky形式主义中构建主操作开始，我们将提取$ l _ {\ infty} $ - 代数，该代数使我们能够从其最小模型中递归计算出扰动者的扩展。然后，在此过程中获得的毛勒 - 卡丹动作将激发所有树级散射幅度的生成函数。这种结构有两个有趣的结果：通过戴克单词的本地化，用于全流量振幅的生成器；以及与$ n $ gluons一起使用任意极化的费米和标量线的封闭表达式。
In this work we present an algebraic approach to the dynamics and perturbation theory at tree-level for gauge theories coupled to matter. The field theories we will consider are: Chern-Simons-Matter, Quantum Chromodynamics, and scalar Quantum Chromodynamics. Starting with the construction of the master action in the classical Batalin-Vilkovisky formalism, we will extract the $L_{\infty}$-algebra that allow us to recursively calculate the perturbiner expansion from its minimal model. The Maurer-Cartan action obtained in this procedure will then motivate a generating function for all the tree-level scattering amplitudes. There are two interesting outcomes of this construction: a generator for fully-flavoured amplitudes via a localisation on Dyck words; and closed expressions for fermion and scalar lines attached to $n$-gluons with arbitrary polarisations.
