D-branes in Topological Minimal Models: the Landau-Ginzburg Approach

TL;DR

This work develops a Landau-Ginzburg approach to D-branes in topological ADE minimal models by encoding B-branes as CDG matrix factorizations of the superpotential W. It delivers an (almost) complete B-brane classification for A-type models, explicit constructions for D- and E-type branes, and exact disk correlators and boundary OPE algebras via a residue-type formula, then matches these results with Cardy B-branes from boundary-state CFT, notably showing that parity reversal (adding a square to W) corresponds to Z2 orbifolding and aligns MM_k/MM_k/Z_2 with LG models having W=x^n−y^2 and W=z^n, respectively. The paper clarifies the open- vs closed-string distinctions across orbifolded theories, establishes concrete correspondences between LG and RCFT branes, and sets up directions for Gepner-model generalizations and orbifold correlators. These results provide a robust bridge between algebraic (CDG) descriptions of branes and CFT boundary states, enabling precise computations of BRST-closed sectors and topological disk amplitudes in a broad class of models.

Abstract

We study D-branes in topologically twisted N=2 minimal models using the Landau-Ginzburg realization. In the cases of A and D-type minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in E-type minimal models. We compare our results with the boundary state formalism, where possible, and find agreement.