Open-closed field algebras

Details Open-closed field algebras Open-closed field algebras

2006-10-09

arxiv.org/abs/math/0610293v3

Commun. Math. Phys. 280, 207-261 (2008)

Mathematics

Quantum Algebra

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

Scientific paper

10.1007/s00220-008-0446-0

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.

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