OPERATOR PRODUCT EXPANSIONS IN THE 2-DIMENSIONAL O(N) NONLINEAR SIGMA-MODEL

The short-distance singularity of the product of a composite scalar fi eld that deforms a field theory and an arbitrary composite field can b e expressed geometrically by the beta functions, anomalous dimensions, and a connection on the theory space. Using this relation, we compute the connection perturbatively for the O(N) non-linear sigma model in two dimensions. We show that the connection becomes free of singularit ies at zero temperature only if we normalize the composite fields so t hat their correlation functions have well-defined limits at zero tempe rature.