Motivated by string field theory, we explore various algebraic aspects of higher spin theory and Vasiliev equation in terms of homotopy algebras. We present a systematic study of unfolded formulation developed for the higher spin equation in terms of the Maurer-Cartan equation associated to differential forms valued in L-infinity algebras. The elimination of auxiliary variables of Vasiliev equation is analyzed through homological perturbation theory. This leads to a closed combinatorial graph formula for all the vertices of higher spin equations in the unfolded formulation. We also discover a topological quantum mechanics model whose correlation functions give deformed higher spin vertices at first order.

中文翻译：

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高自旋理论中的同伦代数

受弦场理论的启发，我们根据同伦代数探索了高自旋理论和 Vasiliev 方程的各种代数方面。我们根据与 L 无穷代数中的微分形式相关联的 Maurer-Cartan 方程，对为更高自旋方程开发的展开公式进行了系统研究。利用同调微扰理论分析了Vasiliev方程辅助变量的消去问题。这导致展开公式中更高自旋方程的所有顶点的闭合组合图公式。我们还发现了一个拓扑量子力学模型，其相关函数在一阶给出变形的更高自旋顶点。