CONFORMAL FIELD-THEORY OF TWISTED VERTEX OPERATORS

The Z2-twisted bosonic conformal field theory associated with a d-dimensional momentum lattice Λ is constructed explicitly. A complete system of vertex operators (conformal fields) which describes this theory on the Riemann sphere is given and is demonstrated to form a mutually local set when d is a multiple of 8, Λ is even, and √2Λ* is also even. (This last condition is weaker than self-duality for Λ, a further requirement which may be necessary for the theory to be defined on higher-genus surfaces.) The construction and properties of cocycle operators are described. Locality implies the closure of the operator product expansion, and thus that all the weight-one fields are guaranteed to close to form an affine algebra. Applications are to the construction of the natural module of Frenkel et al. for the Monster group, and to an improved understanding of twist fields in relation to gauge algebras in string theory. © 1990.