  The short-distance singularity of the product of a composite scalar field
that deforms a field theory and an arbitrary composite field can be 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 singularities at zero temperature only if we
normalize the composite fields so that their correlation functions have
well-defined limits at zero temperature.
