Stringy K\"ahler Moduli for the Pfaffian-Grassmannian Correspondence

TL;DR

This paper explores the Pfaffian-Grassmannian correspondence in Calabi-Yau 3-folds, constructing derived equivalences through mutations and providing a mirror symmetry interpretation based on physical analysis.

Contribution

It introduces a new framework for understanding derived equivalences in the Pfaffian-Grassmannian setting using mutations and connects it to mirror symmetry insights.

Findings

Constructed derived equivalences via mutations of exceptional collections.

Provided a mirror symmetry interpretation for the correspondence.

Linked physical analysis to mathematical structures in Calabi-Yau geometry.

Abstract

The Pfaffian-Grassmannian correspondence relates certain pairs of derived equivalent non-birational Calabi-Yau 3-folds. Given such a pair, I construct a set of derived equivalences corresponding to mutations of an exceptional collection on the relevant Grassmannian, and give a mirror symmetry interpretation, following a physical analysis of Eager, Hori, Knapp, and Romo.