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• W2103209558 abstract "Let V be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that $${mathcal{C}_V}$$ , 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 a certain $${mathbb {C}}$$ -extension of the so-called Swiss-cheese partial dioperad, and we can obtain Ishibashi states easily in such algebras. The Cardy condition can be formulated as an additional condition on such open-closed field algebras in terms of the action of the modular transformation $${S: tau mapsto -frac{1}{tau}}$$ on the space of intertwining operators of V. We then derive a graphical representation of S in the modular tensor category $${mathcal{C}_V}$$ . This result enables us to give a categorical formulation of the Cardy condition and the modular invariance condition for 1-point correlation functions on the torus. Then we incorporate these two conditions and the axioms of the open-closed field algebra over V equipped with nondegenerate invariant bilinear forms into a tensor-categorical notion called the Cardy $${mathcal{C}_V|mathcal{C}_{V otimes V}}$$ -algebra. In the end, we give a categorical construction of the Cardy $${mathcal{C}_V|mathcal{C}_{V otimes V}}$$ -algebra in the Cardy case." @default.
• W2103209558 created "2016-06-24" @default.
• W2103209558 creator A5046524020 @default.
• W2103209558 date "2008-07-24" @default.
• W2103209558 modified "2023-09-26" @default.
• W2103209558 title "Cardy Condition for Open-Closed Field Algebras" @default.
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• W2103209558 doi "https://doi.org/10.1007/s00220-008-0555-9" @default.
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