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High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
A large class of two-dimensional $\mathcal{N}=(2,2)$ 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.
