Defects and D-Brane Monodromies

TL;DR

This paper investigates D-brane monodromies using defect lines in conformal field theories, deriving their geometric actions in moduli spaces through world-sheet methods and matrix factorization techniques.

Contribution

It introduces a world-sheet approach to D-brane monodromies using defect lines, connecting conformal field theory methods with geometric Fourier-Mukai transformations.

Findings

Derived B-brane monodromies in Kahler moduli spaces.

Constructed defects at Landau-Ginzburg points using matrix factorization.

Connected defect actions to Fourier-Mukai transformations at large volume.

Abstract

In this paper D-brane monodromies are studied from a world-sheet point of view. More precisely, defect lines are used to describe the parallel transport of D-branes along deformations of the underlying bulk conformal field theories. This method is used to derive B-brane monodromies in Kahler moduli spaces of non-linear sigma models on projective hypersurfaces. The corresponding defects are constructed at Landau-Ginzburg points in these moduli spaces where matrix factorisation techniques can be used. Transporting them to the large volume phase by means of the gauged linear sigma model we find that their action on B-branes at large volume can be described by certain Fourier-Mukai transformations which are known from target space geometric considerations to represent the corresponding monodromies.