ﻻ يوجد ملخص باللغة العربية
Given a topological modular functor $mathcal{V}$ in the sense of Walker cite{Walker}, we construct vector bundles over $bar{mathcal{M}}_{g,n}$, whose Chern classes define semi-simple cohomological field theories. This construction depends on a determination of the logarithm of the eigenvalues of the Dehn twist and central element actions. We show that the intersection of the Chern class with the $psi$-classes in $bar{mathcal{M}}_{g,n}$ is computed by the topological recursion of cite{EOFg}, for a local spectral curve that we describe. In particular, we show how the Verlinde formula for the dimensions $D_{vec{lambda}}(mathbf{Sigma}_{g,n}) = dim mathcal{V}_{vec{lambda}}(mathbf{Sigma}_{g,n})$ is retrieved from the topological recursion. We analyze the consequences of our result on two examples: modular functors associated to a finite group $G$ (for which $D_{vec{lambda}}(mathbf{Sigma}_{g,n})$ enumerates certain $G$-principle bundles over a genus $g$ surface with $n$ boundary conditions specified by $vec{lambda}$), and the modular functor obtained from Wess-Zumino-Witten conformal field theory associated to a simple, simply-connected Lie group $G$ (for which $mathcal{V}_{vec{lambda}}(mathbf{Sigma}_{g,n})$ is the Verlinde bundle).
In this article, a novel description of the hypergeometric differential equation found from Gelfand-Kapranov-Zelevinskys system (referred to GKZ equation) for Giventals $J$-function in the Gromov-Witten theory will be proposed. The GKZ equation invol
We prove that the topological recursion formalism can be used to quantize any generic classical spectral curve with smooth ramification points and simply ramified away from poles. For this purpose, we build both the associated quantum curve, i.e. the
The purpose of this article is to analyze the connection between Eynard-Orantin topological recursion and formal WKB solutions of a $hbar$-difference equation: $Psi(x+hbar)=left(e^{hbarfrac{d}{dx}}right) Psi(x)=L(x;hbar)Psi(x)$ with $L(x;hbar)in GL_2
We study the $n$-point differentials corresponding to Kadomtsev-Petviashvili tau functions of hypergeometric type (also known as Orlov-Scherbin partition functions), with an emphasis on their $hbar^2$-deformations and expansions. Under the naturall
In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we construct the weighed sums which are given by Orlovs hypergeometric solutio