Quantum spectrum and Gamma structures for quasi-homogeneous polynomials of general type

Author:

Yefeng Shen, Ming Zhang

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), High Energy Physics - Theory (hep-th)

journal:

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date:

2023-09-13 16:00:00

Abstract

Let $W$ be a quasi-homogeneous polynomial of general type and $<J>$ be the cyclic symmetry group of $W$ generated by the exponential grading element $J$. We study the quantum spectrum and asymptotic behavior in Fan-Jarvis-Ruan-Witten theory of the Landau-Ginzburg pair $(W, <J>)$. Inspired by Galkin-Golyshev-Iritani's Gamma conjectures for quantum cohomology of Fano manifolds, we propose Gamma conjectures for Fan-Jarvis-Ruan-Witten theory of general type. We prove the quantum spectrum conjecture and the Gamma conjectures for Fermat homogeneous polynomials and the mirror simple singularities. The Gamma structures in Fan-Jarvis-Ruan-Witten theory also provide a bridge from the category of matrix factorizations of the Landau-Ginzburg pair (the algebraic aspect) to its analytic aspect. We will explain the relationship among the Gamma structures, Orlov's semiorthogonal decompositions, and the Stokes phenomenon.