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arXiv · 2305.03849

Polynomial superpotential for Grassmannian $Gr(k,n)$ from a limit of vertex function

Andrey Smirnov·Alexander Varchenko
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Abstract

In this note we discuss an integral representation for the vertex function of the cotangent bundle over the Grassmannian, $X=T^{*} Gr(k,n)$. This integral representation can be used to compute the $\hbar\to \infty$ limit of the vertex function, where $\hbar$ denotes the equivariant parameter of a torus acting on $X$ by dilating the cotangent fibers. We show that in this limit the integral turns into the standard mirror integral representation for the $A$-series of the Grassmannian $Gr(k,n)$ with the Laurent polynomial Landau-Ginzburg superpotential of Eguchi, Hori and Xiong. We also observe some Dwork type congruences for the coefficients of the $A$-series.

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BibTeXRIS

Andrey Smirnov, Alexander Varchenko. 2023-05-05. Polynomial superpotential for Grassmannian $Gr(k,n)$ from a limit of vertex function. https://arxiv.org/abs/2305.03849

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