标题： 非交换场论中的编织对称性 显示英文标题

标题： Braided Symmetries in Noncommutative Field Theory

摘要： 我们给出了关于$L_\infty$-代数及其在组织经典场论以及弦理论中作为低能有效场论出现的常规非交换规范场论的对称性和动力学方面的教学性介绍。 我们回顾了最近的发展，这些发展将具有辫子规范对称性的场论构造成克服标准非交换理论中几个障碍的新方法，例如对规范代数和物质场的限制。 这些理论可以通过使用 Drinfel'd 扭曲变形理论的技术来构建，我们在一定程度上详细回顾了这些技术，并且它们的对称性和动力学由一种新的同伦代数结构——称为“辫子$L_\infty$-代数”所控制。 我们扩展并详细阐述了围绕这些构造的几个新的理论问题，并提出了三个新的明确例子：标准的非交换标量场论（被视为辫子场论）、任意维度下$BF$理论的辫子版本（被视为高阶规范理论），以及适用于任意规范代数的新非交换 Yang-Mills 理论的辫子版本。 显示英文摘要

摘要： We give a pedagogical introduction to $L_\infty$-algebras and their uses in organising the symmetries and dynamics of classical field theories, as well as of the conventional noncommutative gauge theories that arise as low-energy effective field theories in string theory. We review recent developments which formulate field theories with braided gauge symmetries as a new means of overcoming several obstacles in the standard noncommutative theories, such as the restrictions on gauge algebras and matter fields. These theories can be constructed by using techniques from Drinfel'd twist deformation theory, which we review in some detail, and their symmetries and dynamics are controlled by a new homotopy algebraic structure called a 'braided $L_\infty$-algebra'. We expand and elaborate on several novel theoretical issues surrounding these constructions, and present three new explicit examples: the standard noncommutative scalar field theory (regarded as a braided field theory), a braided version of $BF$ theory in arbitrary dimensions (regarded as a higher gauge theory), and a new braided version of noncommutative Yang-Mills theory for arbitrary gauge algebras.