On the monoidal structure of matrix bi-factorisations

Details On the monoidal structure of matrix bi-factorisations On the monoidal structure of matrix bi-factorisations

2009-09-24

arxiv.org/abs/0909.4381v3

J. Phys. A: Math. Theor. 43 (2010) 275401

Physics

Mathematical Physics

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

Scientific paper

10.1088/1751-8113/43/27/275401

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.

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