标题： LSZ模型的完整解通过拓扑递归 显示英文标题

标题： Complete solution of the LSZ Model via Topological Recursion

摘要： 我们证明了具有四次势的Langmann-Szabo-Zarembo (LSZ)模型，作为非交换空间上量子场论的一个玩具模型，被当作复矩阵模型来理解，遵循Chekhov、Eynard和Orantin的拓扑递归。 通过引入两族相关函数，其中一族对应于拓扑递归中的亚纯微分$\omega_{g,n}$，我们得到了最终导致抽象环方程的Dyson-Schwinger方程，这些方程与其极点结构一起，是拓扑递归的必要条件。 这一策略展示了LSZ模型的精确可解性，为某些量子场论中可积性的特殊性质提供了另一种方法。 我们比较了LSZ模型（具有复场）和Grosse-Wulkenhaar模型（具有厄米场）的环方程之间的差异，以及它们对控制这些模型的特定类型拓扑递归所产生的影响。 显示英文摘要

摘要： We prove that the Langmann-Szabo-Zarembo (LSZ) model with quartic potential, a toy model for a quantum field theory on noncommutative spaces grasped as a complex matrix model, obeys topological recursion of Chekhov, Eynard and Orantin. By introducing two families of correlation functions, one corresponding to the meromorphic differentials $\omega_{g,n}$ of topological recursion, we obtain Dyson-Schwinger equations that eventually lead to the abstract loop equations being, together with their pole structure, the necessary condition for topological recursion. This strategy to show the exact solvability of the LSZ model establishes another approach towards the exceptional property of integrability in some quantum field theories. We compare differences in the loop equations for the LSZ model (with complex fields) and the Grosse-Wulkenhaar model (with hermitian fieldss) and their consequences for the resulting particular type of topological recursion that governs the models.