On the monoidal structure of matrix bi-factorizations

We investigate tensor products of matrix factorizations. This is most naturally done by formulating matrix factorizations in terms of bimodules instead of modules. If the underlying ring is C[x(1), ..., x(N)], we show that bimodule matrix factorizations 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.