Open-closed field algebras

Abstract

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a $\C$-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical constructions of open-closed field algebras over V.

55 pages, largely revised, an old subsection is deleted, a few references are added

References in corpus (5)

• Field Algebras
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Full field algebras
• Constructing quantum vertex algebras
• Full field algebras, operads and tensor categories

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