ﻻ يوجد ملخص باللغة العربية
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 involves a parameter $hbar$, and we will reconstruct it as the WKB expansion from the classical limit $hbarto 0$ via the topological recursion. In this analysis, the spectral curve (referred to GKZ curve) plays a central role, and it can be defined as the critical point set of the mirror Landau-Ginzburg potential. Our novel description is derived via the duality relations of the string theories, and various physical interpretations suggest that the GKZ equation is identified with the quantum curve for the brane partition function in the cohomological limit. As an application of our novel picture for the GKZ equation, we will discuss the Stokes matrix for the equivariant $mathbb{C}textbf{P}^{1}$ model and the wall-crossing formula for the total Stokes matrix will be examined. And as a byproduct of this analysis we will study Dubrovins conjecture for this equivariant model.
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
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 determ
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
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
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