Riemann surfaces with boundaries and the theory of vertex operator algebras

Details Riemann surfaces with boundaries and the theory of vertex operator algebras Riemann surfaces with boundaries and the theory of vertex operator algebras

2002-12-22

arxiv.org/abs/math/0212308v3

Mathematics

Quantum Algebra

26 pages. Final version to appear in Vertex Operator Algebras in Mathematics and Physics, Fields Institute Communications, Ame

Scientific paper

The connection between Riemann surfaces with boundaries and the theory of vertex operator algebras is discussed in the framework of conformal field theories defined by Kontsevich and Segal and in the framework of their generalizations in open string theory and boundary conformal field theory. We present some results, problems, conjectures, their conceptual implications and meanings in a program to construct these theories from representations of vertex operator algebras.

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