Abstract
We summarize the main results of our investigation of B-type topological Landau-Ginzburg models whose target is an arbitrary open Riemann surface. Such a Riemann surface need not be affine algebraic and in particular it may have infinite genus or an infinite number of Freudenthal ends. Under mild conditions on the Landau-Ginzburg superpotential, we give a complete description of the triangulated structure of the category of topological D-branes in such models as well as counting formulas for the number of topological D-branes considered up to relevant equivalence relations.
Highlights
It is well-known [1, 2] that classical B-type topological Landau-Ginzburg (LG) models with Dbranes can be associated to any pair (X, W ), where X is a non-compact Kahler manifold and W : X → C is a non-constant holomorphic function defined on X
When the canonical line bundle of X is holomorphically trivial and the critical set of W is compact, it is expected that the quantization of such models produces a non-anomalous two-dimensional topological field theory (2d TFT) which obeys the general axioms introduced in [3] and is characterized entirely by an open-closed TFT datum, an algebraic structure subject to certain axioms which encode the sewing constraints of the TFT
As shown in [2], path integral arguments lead to a proposal for the open-closed TFT datum of the quantum B-type LG model defined by such a pair (X, W ), a proposal which was clarified and analyzed mathematically in [4, 5]
Summary
It is well-known [1, 2] that classical B-type topological Landau-Ginzburg (LG) models with Dbranes can be associated to any pair (X, W ), where X is a non-compact Kahler manifold and W : X → C is a non-constant holomorphic function defined on X. Since any open Riemann surface is Stein and holomorphically parallelizable ( Calabi-Yau), this fits into the class of models considered in [7], whose TFT datum admits the simplified description discussed in loc. In this contribution, we outline our investigation of B-type LG models with open Riemann surface target [9], which in turn relies on algebraic results derived for a large class of rings in references [10, 11]. The topological LG models discussed are the most general non-anomalous B-type LG models with non-singular complex one-dimensional target
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