论文标题
通过拓扑递归的LSZ模型的完整解决方案
Complete solution of the LSZ Model via Topological Recursion
论文作者
论文摘要
我们证明，具有四分之一电位的Langmann-Szabo-Zarembo（LSZ）模型，这是一种量子场理论的玩具模型，该模型是抓住复杂矩阵模型的非交通空间的量子场理论，服从于Chekhov，Eynard和Orantin的拓扑结构。通过引入两个相关函数的家族，一个对应于拓扑递归的Meromororphic差异$ω_{g，n} $，我们获得了Dyson-Schwinger方程，最终导致抽象的循环方程与其极点结构，其极点结构，是拓扑递归的必要条件。该策略显示LSZ模型的确切可溶性为某些量子场理论中的集成性特性提供了另一种方法。我们比较了LSZ模型（具有复杂场）和Grosse-Wulkenhaar模型（与Hermitian Fieldss）的循环方程式的差异及其对控制模型的特定类型的拓扑递归的后果。
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 $ω_{g,n}$ 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.
