Abstract
New conformal field theories are defined as a generalization of the vertex operator construction to arbitrary level, k, and arbitrary simple Lie algebra. Exact scaling dimensions and partition functions are given in terms of the string functions of affine algebra. The theories have a discrete symmetry group which is the root lattice modulo k times the long roots lattice. Twisted partition functions are given, and the general solutions to modular invariance are described as orbifolds of principal ones.
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