The Kapustin-Li formula revisited

Journal article

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.

Authors: Dyckerhoff, T; Murfet, D

• Journal: Advances in Mathematics
• Volume: 231
• Issue: 3-4
• Pages: 1858-1885
• Publication date: 2010-04-05
• DOI: 10.1016/j.aim.2012.07.021
• EISSN: 1090-2082
• ISSN: 0001-8708
• Language: English
• Keywords: math.AC; math.AG