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 Kähler 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 factorization techniques can
be used. Transporting them to the large volume phase by means of
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.