Landau-Ginzburg Realization of Open String TFT

TL;DR

The paper provides a concrete open-closed TFT realization via a one-variable B-type Landau-Ginzburg model with D2-branes. It shows that brane configurations are classified by factorizations of the bulk superpotential $W$ and constructs the corresponding open-string chiral rings containing both bosonic and fermionic generators, with relations dictated by the factorization. It verifies that disk correlators obey topological sewing constraints and establishes an adjoint bulk-boundary map that enforces Cardy consistency. Finally, it connects the LG construction to Kontsevich's triangulated category of D-branes, giving a physical realization of the abstract categorical framework and recovering BCFT spectra in the appropriate limits.

Abstract

We investigate B-type topological Landau-Ginzburg theory with one variable, with D2-brane boundary conditions. We find that the allowed brane configurations are determined in terms of the possible factorizations of the superpotential, and compute the corresponding open string chiral rings. These are characterized by bosonic and fermionic generators that satisfy certain relations. Moreover we show that the disk correlators, being continuous functions of deformation parameters, satisfy the topological sewing constraints, thereby proving consistency of the theory. In addition we show that the open string LG model is, in its content, equivalent to a certain triangulated category introduced by Kontsevich, and thus may be viewed as a concrete physical realization of it.

Figures (1)

• Figure 1: The Cardy condition requires that the factorization of the topological annulus amplitude on closed and open string channels yields the same result. We show in the text that its solution is intimately tied to the factorization condition $W=EJ$ of the LG superpotential.