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arXiv · 1407.7254

Matrix factorisations for rational boundary conditions by defect fusion

Nicolas Behr·Stefan Fredenhagen
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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.

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Nicolas Behr, Stefan Fredenhagen. 2014-07-27. Matrix factorisations for rational boundary conditions by defect fusion. https://doi.org/10.1007/jhep05(2015)055

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