Communications in Mathematical Physics

, Volume 250, Issue 3, pp 433–471

Open-String Vertex Algebras, Tensor Categories and Operads

Article

DOI: 10.1007/s00220-004-1059-x

Cite this article as:
Huang, YZ. & Kong, L. Commun. Math. Phys. (2004) 250: 433. doi:10.1007/s00220-004-1059-x

Abstract

We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are “open-string-theoretic”, “noncommutative” generalizations of the notions of vertex algebra and of conformal vertex algebra. Given an open-string vertex algebra, we show that there exists a vertex algebra, which we call the “meromorphic center,” inside the original algebra such that the original algebra yields a module and also an intertwining operator for the meromorphic center. This result gives us a general method for constructing open-string vertex algebras. Besides obvious examples obtained from associative algebras and vertex (super)algebras, we give a nontrivial example constructed from the minimal model of central charge Open image in new window We establish an equivalence between the associative algebras in the braided tensor category of modules for a suitable vertex operator algebra and the grading-restricted conformal open-string vertex algebras containing a vertex operator algebra isomorphic to the given vertex operator algebra. We also give a geometric and operadic formulation of the notion of grading-restricted conformal open-string vertex algebra, we prove two isomorphism theorems, and in particular, we show that such an algebra gives a projective algebra over what we call the “Swiss-cheese partial operad.”

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA

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