The Pfaffian-Grassmannian derived equivalence

TL;DR

This paper establishes a derived equivalence between two families of Calabi-Yau threefolds, constructed from dual hyperplane sections of Grassmannian G(2,7) and Pfaffian Pf(7), confirming a long-standing physicist conjecture.

Contribution

It provides the first proven example of a derived equivalence between non-birational Calabi-Yau threefolds, linking dual geometric constructions.

Findings

Derived equivalence between G(2,7) and Pf(7) Calabi-Yau threefolds.

Supports the conjecture that these families share the same mirror.

First proof of such an equivalence for non-birational Calabi-Yau threefolds.

Abstract

We argue that there exists a derived equivalence between Calabi-Yau threefolds obtained by taking dual hyperplane sections (of the appropriate codimension) of the Grassmannian G(2, 7) and the Pfaffian Pf(7). The existence of such an equivalence has been conjectured by physicists for almost ten years, as the two families of Calabi-Yau threefolds are believed to have the same mirror. It is the first example of a derived equivalence between Calabi-Yau threefolds which are provably non-birational.