On the monoidal structure of matrix bi-factorizations

Abstract

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 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 = xd is an 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.