Monodromy of Calabi-Yau threefold flops via grade restriction rule and their quantum Kahler moduli

TL;DR

This paper derives exact formulas for monodromies of Calabi-Yau threefold flops using grade restriction rules, window categories, and hemisphere partition functions, revealing their relation to quantum Kähler moduli and torus link groups.

Contribution

It introduces a general formula for monodromy actions on B-brane charges in Calabi-Yau threefolds using advanced categorical and physical techniques.

Findings

Derived explicit monodromy formulas for Calabi-Yau flops.

Connected monodromies to the fundamental group of nested torus links.

Refined monodromy descriptions using discriminant structures in quantum Kähler moduli.

Abstract

We present exact expressions, based on the grade restriction rule and window categories, for monodromies associated to certain Calabi-Yau threefold flops. We show a general formula for the monodromy action on the lattice of B-brane charges, based on the hemisphere partition function for abelian and nonabelian gauged linear sigma models. We exploit the explicit form of the discriminant in the quantum K\"ahler moduli to further refine the form of the monodromies, in several examples, using their relation to the fundamental group of nested torus links.