The Pfaffian-Grassmannian equivalence revisited

Abstract

We give a new proof of the 'Pfaffian-Grassmannian' derived equivalence between certain pairs of non-birational Calabi-Yau threefolds. Our proof follows the physical constructions of Hori and Tong, and we factor the equivalence into three steps by passing through some intermediate categories of (global) matrix factorizations. The first step is global Knoerrer periodicity, the second comes from a birational map between Landau-Ginzburg B-models, and for the third we develop some new techniques.

Improved exposition, minor corrections. 32 pages

References in corpus (2)

• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Homological projective duality for Grassmannians of lines

Cited by in corpus (12)

• A Mathematical Theory of the Gauged Linear Sigma Model
• Derived Kn"orrer periodicity and Orlov's theorem for gauged Landau-Ginzburg models
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Derived equivalent Hilbert schemes of points on K3 surfaces which are not birational
• Two-dimensional gauge dynamics and the topology of singular determinantal varieties
• Hori-mological projective duality
• Motives and the Pfaffian-Grassmannian equivalence
• Hemisphere Partition Function and Monodromy
• The homological projective dual of Sym^2 P(V)
• The generalized roof F(1,2,n): Hodge structures and derived categories
• Stringy Kähler Moduli for the Pfaffian-Grassmannian Correspondence
• Holomorphic field theories and higher algebra