Rigidity and defect actions in Landau-Ginzburg models

Details Rigidity and defect actions in Landau-Ginzburg models Rigidity and defect actions in Landau-Ginzburg models

2010-06-29

arxiv.org/abs/1006.5609v2

Comm. Math. Phys. 310 (2012) 135-179

Physics

High Energy Physics

High Energy Physics - Theory

53 pages; v2: clarified exposition of pivotal structures, corrected proof of theorem 2.13, added remark 3.9; version to appear

Scientific paper

10.1007/s00220-011-1403-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.

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