Matrix factorisations and permutation branes

TL;DR

This paper explores the use of matrix factorisations to describe B-type D-branes in tensor products of N=2 minimal models, linking algebraic and conformal field theory descriptions, and applies this to Gepner models.

Contribution

It establishes a connection between matrix factorisations and boundary states in conformal field theory for B-type D-branes, including explicit examples in Gepner models.

Findings

D0- and D2-branes are described by permutation boundary states.

In some models, D2-brane images generate the full charge lattice.

The approach applies to models like the quintic.

Abstract

The description of B-type D-branes on a tensor product of two N=2 minimal models in terms of matrix factorisations is related to the boundary state description in conformal field theory. As an application we show that the D0- and D2-brane for a number of Gepner models are described by permutation boundary states. In some cases (including the quintic) the images of the D2-brane under the Gepner monodromy generate the full charge lattice.