Defects and D-Brane Monodromies

TL;DR

The paper develops a world-sheet defect framework to study how B-type D-branes vary under loops in Kahler moduli space, focusing on LG/GPSM setups for Calabi–Yau hypersurfaces. By constructing B-type defects at Landau-Ginzburg points and transporting them through gauged linear sigma models to the large-volume phase, the authors show that the induced brane monodromies are precisely Fourier-Mukai transforms on $D^b(X)$, in agreement with geometric predictions. It provides concrete LG realizations for LG and conifold monodromies, and a universal construction of conifold-like defects in general ${ m N}=(2,2)$ CFTs, tying defect fusion to derived-category autoequivalences. The approach offers a computationally transparent and modular route to D-brane monodromies, with potential extensions to more complex moduli spaces and brane configurations, including D0-branes and K-theory torsion phenomena.

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.