English

On the monoidal structure of matrix bi-factorisations

Mathematical Physics 2014-11-20 v3 High Energy Physics - Theory math.MP Quantum Algebra

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.

Keywords

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

R2 v1 2026-06-21T13:49:54.350Z