A Global Operator Approach to Wess-Zumino-Novikov-Witten models

摘要

We present a global operator approach to Wess-Zumino-Novikov models for compact Riemann surfaces of arbitrary genus g with N marked points. The approach is based on the multipoint Krichever-Novikov algebras of global meromorphic functions and vector fields, and the global algebras of affine type and their representations. Using the global Sugawara construction and the identification of a certain subspace of the vector field algebra with the tangent space to the moduli space of the geometric data, the Knizhnik-Zamalodchikov connection is defined. For fermionic representations it defines a projectively flat connection on the vector bundle of conformal blocks. The presented work is joint work with Oleg Sheinman.