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On the monoidal structure of matrix bi-factorisations
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.Comment: 43 pages; v2: corrected a mistake in sec. 1 and app. A.1, the results
are unaffected; v3: minor change