Matrix factorisations and D-branes on K3

TL;DR

The paper addresses how B-type D-branes on K3 can be understood coherently across three descriptions: geometry of hypersurfaces in weighted projective spaces, matrix factorisations in Landau-Ginzburg models, and conformal field theory on the T^4/\mathbb{Z}_4 orbifold line. It shows that tensor and certain permutation branes admit global deformations across moduli, while other branes are obstructed in a way that matches RR-charge considerations; the rank of the Picard lattice is recovered by combining geometric and MF data, and a detailed dictionary between Gepner points and torus orbifold realizations is developed. The results demonstrate the predictive power of matrix factorisations for B-branes at generic points in moduli space and establish concrete links to CFT boundary states, including obstructions and special loci where deformations are allowed. Overall, the work strengthens the bridge between LG/MF methods and geometric/CFT descriptions of D-branes on K3 and highlights the role of RR charges in moduli-deformation constraints.

Abstract

D-branes on K3 are analysed from three different points of view. For deformations of hypersurfaces in weighted projected space we use geometrical methods as well as matrix factorisation techniques. Furthermore, we study the D-branes on the T^4/\Z_4 orbifold line in conformal field theory. The behaviour of the D-branes under deformations of the bulk theory are studied in detail, and good agreement between the different descriptions is found.