Matrix factorisations and permutation branes

TL;DR

The work establishes a detailed bridge between matrix factorisations in Landau–Ginzburg theories and boundary states in Gepner-model CFTs, identifying D0- and D2-branes with permutation branes and showing that Gepner monodromy images can generate the full RR charge lattice in several examples. By analyzing rank-1 and tensor-product factorisations, the authors derive open-string spectra, brane flows, and g-factors, and verify stability at the Gepner point. The Gepner-model construction demonstrates how permutation branes extend charge lattices beyond Recknagel–Schomerus branes and clarifies when they suffice to capture all charges. The results unify matrix-factorisation, geometry via Orlov’s category, and conformal-field-theory techniques, offering a concrete path to understand brane charges and stability across Calabi–Yau compactifications.

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.