论文标题
两种用于斑点拓扑递归中扰动扩张的方法
Two Approaches For a Perturbative Expansion in Blobbed Topological Recursion
论文作者
论文摘要
在本文中，我们继续对四分之一的Kontsevich模型进行扰动分析。我们研究了$ m = 1,2 $，遵守斑点拓扑递归的$ω^{（0）} _ m $。我们计算它们的膨胀，并检查它们与色带权重和带有QFT中扰动理论的常见方法获得的等效性，在使用Mathematica的耦合中最多可达第五阶。 此外，我们还提供了置换对$（α，σ）$的目录，该$（α，σ）$编码所有5660个真空色带图，这些图形有助于自由能$ \ Mathcal {f}^{（g）} $与属$ g \ geq 0 $ fifth off fifth of Fifth of Fifth fording the Expent cormon的功能，并考虑到一般方法$ g _ {\ dots} $。这是迈向四分之一kontsevich模型中功能区扩展计算的第一步。
In this paper we continue the perturbative analysis of the quartic Kontsevich model. We investigate meromorphic functions $Ω^{(0)}_m$ with $m=1,2$, that obey blobbed topological recursion. We calculate their expansions and check their equivalence to sums of ribbon graph weights, which are obtained with common methods of perturbation theory in QFT, up to fifth order in the coupling using Mathematica. Furthermore, we provide a catalog of permutation pairs $(α,σ)$, which encode all 5660 vacuum ribbon graphs that contribute to the free energy $\mathcal{F}^{(g)}$ with genus $g\geq 0$ up to fifth order and begin to expand upon the used methods to also consider ribbon graphs of general correlation functions $G_{\dots}$. This is a first step towards automation of the calculation of ribbon graph expansions in the quartic Kontsevich model.
