%0 Journal Article
%T Rigidity and defect actions in Landau-Ginzburg models
%A Nils Carqueville
%A Ingo Runkel
%J Mathematics
%D 2010
%I arXiv
%R 10.1007/s00220-011-1403-x
%X Studying two-dimensional field theories in the presence of defect lines naturally gives rise to monoidal categories: their objects are the different (topological) defect conditions, their morphisms are junction fields, and their tensor product describes the fusion of defects. These categories should be equipped with a duality operation corresponding to reversing the orientation of the defect line, providing a rigid and pivotal structure. We make this structure explicit in topological Landau-Ginzburg models with potential x^d, where defects are described by matrix factorisations of x^d-y^d. The duality allows to compute an action of defects on bulk fields, which we compare to the corresponding N=2 conformal field theories. We find that the two actions differ by phases.
%U http://arxiv.org/abs/1006.5609v2