Matrix factorisations and D-branes on K3

TL;DR

This paper investigates D-branes on K3 surfaces using geometric, matrix factorisation, and conformal field theory methods, analyzing their behavior under deformations and establishing consistency across approaches.

Contribution

It provides a comprehensive comparison of D-brane descriptions on K3 via geometry, matrix factorisation, and conformal field theory, highlighting their agreement.

Findings

Consistent descriptions of D-branes across different frameworks.

Detailed analysis of D-brane behavior under bulk deformations.

Validation of matrix factorisation techniques in D-brane studies.

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.