9 research outputs found
On the monoidal structure of matrix bi-factorisations
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.Comment: 43 pages; v2: corrected a mistake in sec. 1 and app. A.1, the results
are unaffected; v3: minor change
Cardy condition for open-closed field algebras
Let be a vertex operator algebra satisfying certain reductivity and
finiteness conditions such that , the category of V-modules, is
a modular tensor category. We study open-closed field algebras over V equipped
with nondegenerate invariant bilinear forms for both open and closed sectors.
We show that they give algebras over certain \C-extension of the Swiss-cheese
partial dioperad, and we obtain Ishibashi states easily in such algebras. We
formulate Cardy condition algebraically in terms of the action of the modular
transformation on the space of intertwining
operators. We then derive a graphical representation of S in the modular tensor
category . This result enables us to give a categorical
formulation of Cardy condition and modular invariant conformal full field
algebra over . Then we incorporate the modular invariance condition
for genus-one closed theory, Cardy condition and the axioms for open-closed
field algebra over V equipped with nondegenerate invariant bilinear forms into
a tensor-categorical notion called Cardy -algebra. We also give a categorical construction of Cardy
-algebra in Cardy case.Comment: 70 page, 105 figures, references are updated. less typos, to appear
in Comm. Math. Phy
Twisted K-Theory and Modular Invariants: I Quantum Doubles of Finite Groups
Summary. A twisted vector-bundle approach to α-induction and modular invari-ants. 1 Introduction and statement of results The Verlinde algebra is central to conformal field theory and consequently also to the braided subfactor approach to modular invariants. In the braided sub-factor approach to modular invariants one has first a factor N, which we can take to be type III, and a non-degenerately braided system of endomorphism