Differential models for B-type open-closed topological Landau-Ginzburg theories
arXiv:1610.09103 · doi:10.1007/s00220-018-3137-5
Abstract
We propose a family of differential models for B-type open-closed topological Landau-Ginzburg theories defined by a pair , where is any non-compact Calabi-Yau manifold and is any holomorphic complex-valued function defined on whose critical set is compact. The models are constructed at cochain level using smooth data, including the twisted Dolbeault algebra of polyvector valued forms and a twisted Dolbeault category of holomorphic factorizations of . We give explicit proposals for cochain level versions of the bulk and boundary traces and for the bulk-boundary and boundary-bulk maps of the Landau-Ginzburg theory. We prove that most of the axioms of an open-closed topological field theory are satisfied on cohomology and conjecture that the remaining axioms are also satisfied.
arXiv comment64 pages
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