Matrix factorisations for rational boundary conditions by defect fusion

  • Nicolas BehrEmail author
  • Stefan Fredenhagen
Open Access
Regular Article - Theoretical Physics


A large class of two-dimensional \( \mathcal{N}=\left(2,\ 2\right) \) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the SU(3)/U(2) Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the SU(3)/U(2) model.


D-branes Conformal Field Models in String Theory Tachyon Condensation Topological Field Theories 


Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of MathematicsHeriot-Watt UniversityEdinburghU.K.
  2. 2.Maxwell Institute for Mathematical SciencesEdinburghU.K.
  3. 3.Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-InstitutGolmGermany

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