Rigidity and defect actions in Landau-Ginzburg models

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 N=2 conformal field theories. We find that the two actions differ by phases.

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

References in corpus (3)

• Duality and defects in rational conformal field theory
• B-type defects in Landau-Ginzburg models
• The fusion algebra of bimodule categories

Cited by in corpus (10)

• Adjunctions and defects in Landau-Ginzburg models
• String-net models for non-spherical pivotal fusion categories
• Computing Khovanov-Rozansky homology and defect fusion
• Orbifold equivalent potentials
• Pushing forward matrix factorisations
• Domain walls between 3d phases of Reshetikhin-Turaev TQFTs
• Realizing IR theories by projections in the UV
• Matrix factorisations for rational boundary conditions by defect fusion
• Reshetikhin-Turaev TQFTs close under generalised orbifolds
• Noninvertible symmetries in the B model TFT