We summarise some of our recent works on ‐algebras and quasi‐groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of ‐algebras, we discuss their Maurer–Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin–Vilkovisky formalism. As examples, we explore higher Chern–Simons theory and Yang–Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of ‐quasi‐isomorphisms, and we propose a twistor space action.

中文翻译：

---

‐代数，BV形式主义和古典场

我们总结了一些关于代数和准群的最新著作，涉及较高的主束及其在扭转理论和规范理论中的应用。特别是，在对代数进行了闪电般的回顾之后，我们讨论了他们的Maurer-Cartan理论，并解释说，在这种情况下，可以借助Batalin-Vilkovisky形式主义来重新定义任何承认行为的经典场论。作为示例，我们探索高级的Chern–Simons理论和Yang–Mills理论。我们还解释了如何将这些思想与扭力理论相结合，以借助准同构在四个和六个维度上形成最大的超保形规范理论，并提出了扭力空间作用。