N-POINT G-LOOP VERTEX FOR A FREE FERMIONIC THEORY WITH ARBITRARY SPIN

We use the sewing procedure of the operator formalism to construct explicitly the N-point g-loop vertex VN;g for a free fermionic (b,c)-system with conformal weight (λ, 1-λ). We show that this vertex has the structure we expect from geometrical arguments. We obtain also several geometrical objects, e.g. the holomorphic λ-differentials on an arbitrary Riemann surface, which turn out to be expressed as a Poincaré θ-series over all elements of the Schottky group. From VN;g we compute explicitly correlation functions for our system, finding agreement with the geometrical procedure. © 1990.