  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.
