English

Rigidity and defect actions in Landau-Ginzburg models

High Energy Physics - Theory 2012-02-09 v2 Mathematical Physics math.MP Quantum Algebra

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.

Keywords

Cite

@article{arxiv.1006.5609,
  title  = {Rigidity and defect actions in Landau-Ginzburg models},
  author = {Nils Carqueville and Ingo Runkel},
  journal= {arXiv preprint arXiv:1006.5609},
  year   = {2012}
}

Comments

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

R2 v1 2026-06-21T15:42:24.830Z