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.
Cite
@article{arxiv.0909.4381,
title = {On the monoidal structure of matrix bi-factorisations},
author = {Nils Carqueville and Ingo Runkel},
journal= {arXiv preprint arXiv:0909.4381},
year = {2014}
}
Comments
43 pages; v2: corrected a mistake in sec. 1 and app. A.1, the results are unaffected; v3: minor changes