论文标题
四分之一的Kontsevich模型I的斑点拓扑递归：循环方程式和猜想
Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
论文作者
论文摘要
我们提供了有力的猜想，即Kontsevich的矩阵Airy功能的类似物，即Cutic潜在的$ \ Mathrm {tr}（φ^3）$替换为Quartic $ \ mathrm {trm {tr}（φ^4）$替换，遵守Blobbed Budbed topolical of Borot of Borot and Shadrin和Shadrin和Shadrin。我们在四分之一的Kontsevich中确定了三个相关函数的家族，我们为其建立了交织的循环方程。一个系列由对称的meromorthic差异形式组成$ω__{g，n} $由属标记的复杂曲线标记点的数量。我们将所有循环方程式的解决方案减少到对残基的直接评估。在所有评估的情况下，$ω_{g，n} $由一个零件组成，该零件在分支点上满足拓扑递归的通用公式，以及在RAMIFIENT PONTICE的一部分全体形态，我们为其提供明确的残基公式。
We provide strong evidence for the conjecture that the analogue of Kontsevich's matrix Airy function, with the cubic potential $\mathrm{Tr}(Φ^3)$ replaced by a quartic term $\mathrm{Tr}(Φ^4)$, obeys the blobbed topological recursion of Borot and Shadrin. We identify in the quartic Kontsevich model three families of correlation functions for which we establish interwoven loop equations. One family consists of symmetric meromorphic differential forms $ω_{g,n}$ labelled by genus and number of marked points of a complex curve. We reduce the solution of all loop equations to a straightforward but lengthy evaluation of residues. In all evaluated cases, the $ω_{g,n}$ consist of a part with poles at ramification points which satisfies the universal formula of topological recursion, and of a part holomorphic at ramification points for which we provide an explicit residue formula.
