On the monoidal structure of matrix bi-factorisations

Abstract

We investigate tensor products of matrix factorisations. This is most naturally done by formulating matrix factorisations in terms of bimodules instead of modules. If the underlying ring is C[x_1,...,x_N] we show that bimodule matrix factorisations form a monoidal category. This monoidal category has a physical interpretation in terms of defect lines in a two-dimensional Landau-Ginzburg model. There is a dual description via conformal field theory, which in the special case of W=x^d is an N=2 minimal model, and which also gives rise to a monoidal category describing defect lines. We carry out a comparison of these two categories in certain subsectors by explicitly computing 6j-symbols.

43 pages; v2: corrected a mistake in sec. 1 and app. A.1, the results are unaffected; v3: minor changes

References in corpus (3)

• Duality and defects in rational conformal field theory
• Topological defects for the free boson CFT
• B-type defects in Landau-Ginzburg models

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• Matrix factorisations for rational boundary conditions by defect fusion
• Differential models for B-type open-closed topological Landau-Ginzburg theories
• Attractor Flows from Defect Lines
• Fusion of interfaces in Landau-Ginzburg models: a functorial approach