论文标题
四分之一的Kontsevich模型的扰动和几何分析
Perturbative and Geometric Analysis of the Quartic Kontsevich Model
论文作者
论文摘要
The analogue of Kontsevich's matrix Airy function, with the cubic potential $\operatorname{Tr}\big(Φ^3\big)$ replaced by a quartic term $\operatorname{Tr}\big(Φ^4\big)$ with the same covariance, provides a toy model for quantum field theory in which all correlation functions can be computed exactly and explicitly.在本文中，我们表明，相关函数的多项式分别是由快速增长的Feynman Ribbon图系列给出的，总结到更简单，更高度结构化的表达式。这些表达式与猜想遵守斑点拓扑递归的meromorthic形式深深相关。此外，我们展示了确切的解决方案如何探索四分之一的Kontsevich模型中的关键现象。
The analogue of Kontsevich's matrix Airy function, with the cubic potential $\operatorname{Tr}\big(Φ^3\big)$ replaced by a quartic term $\operatorname{Tr}\big(Φ^4\big)$ with the same covariance, provides a toy model for quantum field theory in which all correlation functions can be computed exactly and explicitly. In this paper we show that distinguished polynomials of correlation functions, themselves given by quickly growing series of Feynman ribbon graphs, sum up to much simpler and highly structured expressions. These expressions are deeply connected with meromorphic forms conjectured to obey blobbed topological recursion. Moreover, we show how the exact solutions permit to explore critical phenomena in the quartic Kontsevich model.
