Cardy condition for open-closed field algebras. (English) Zbl 1156.81023
The author studies open-closed field algebras over a vertex operator algebra V equipped with nondegenerate invariant bilinear forms for both open and closed sectors. The author proves that the open-closed field algebras give algebras over a certain \(C\)-extension of the so-called Swiss-cheese partial dioperad. The author also derives a graphical representation of \(S\) in the modular tensor category \(Cv\) and a categorical construction of the Cardy algebra in the Cardy case.
Reviewer: Yong-Qing Chen (Shenzhen)
MSC:
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81R15 | Operator algebra methods applied to problems in quantum theory |
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