论文标题
在$ x $ - $ y $ $的对称性相关器中，通过循环插入操作员在拓扑递归中
On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator
论文作者
论文摘要
拓扑递归从某些初始数据$（σ，x，y，b）$中产生一系列对称差分形式（相关器）。我们在初始数据$（σ，x，y，b）$的属$ g = 0 $的相关器与初始数据$（σ，y，x，b）$之间产生的功能关系，其中$ x $和y $互换。通过计算某些中间相关器的功能关系，可以通过循环插入运算符得出功能关系。此外，我们表明我们的结果等效于\ cite {Borot：2021thu}的最新结果，如果$ g = 0 $。因此，我们在以高阶概率的情况下提供了简化的功能关系。
Topological Recursion generates a family of symmetric differential forms (correlators) from some initial data $(Σ,x,y,B)$. We give a functional relation between the correlators of genus $g=0$ generated by the initial data $(Σ,x,y,B)$ and by the initial data $(Σ,y,x,B)$, where $x$ and $y$ are interchanged. The functional relation is derived with the loop insertion operator by computing a functional relation for some intermediate correlators. Additionally, we show that our result is equivalent to the recent result of \cite{Borot:2021thu} in case of $g=0$. Consequently, we are providing a simplified functional relation between generating series of higher order free cumulants and moments in higher order free probability.
