Abstract
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 \({\mathcal N = 2}\) conformal field theories. We find that the two actions differ by phases.
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Carqueville, N., Runkel, I. Rigidity and Defect Actions in Landau-Ginzburg Models. Commun. Math. Phys. 310, 135–179 (2012). https://doi.org/10.1007/s00220-011-1403-x
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DOI: https://doi.org/10.1007/s00220-011-1403-x