The Kapustin-Li formula revisited

Abstract

We provide a new perspective on the Kapustin-Li formula for the duality pairing on the morphism complexes in the matrix factorization category of an isolated hypersurface singularity. In our context, the formula arises as an explicit description of a local duality isomorphism, obtained by using the basic perturbation lemma and Grothendieck residues. The non-degeneracy of the pairing becomes apparent in this setting. Further, we show that the pairing lifts to a Calabi-Yau structure on the matrix factorization category. This allows us to define topological quantum field theories with matrix factorizations as boundary conditions.

28 pages, 3 figures, comments welcome

References in corpus (6)

• Compact generators in categories of matrix factorizations
• On the Classification of Topological Field Theories
• On the perturbation lemma, and deformations
• Chern characters and Hirzebruch-Riemann-Roch formula for matrix factorizations
• Matrix factorisations and open topological string theory
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Cited by in corpus (13)

• Compact generators in categories of matrix factorizations
• Adjunctions and defects in Landau-Ginzburg models
• Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)
• Pushing forward matrix factorisations
• A category of kernels for equivariant factorizations and its implications for Hodge theory
• Hybrid models for homological projective duals and noncommutative resolutions
• Calabi-Yau structures on categories of matrix factorizations
• Differential models for B-type open-closed topological Landau-Ginzburg theories
• On B-type open-closed Landau-Ginzburg theories defined on Calabi-Yau Stein manifolds
• Pairings in mirror symmetry between a symplectic manifold and a Landau-Ginzburg $B$-model
• Chern Characters for Twisted Matrix Factorizations and the Vanishing of the Higher Herbrand Difference
• Chern character for matrix factorizations via Chern-Weil
• Foams, iterated wreath products, field extensions and Sylvester sums