DEVIATIONS FROM SCALE-INVARIANCE NEAR A GENERAL CONFORMAL BACKGROUND

Deviations from scale invariance resulting from small perturbations of a general two-dimensional conformal field theory are studied. They ar e expressed in terms of beta-functions for the renormalization of gene ral couplings under a local change of scale. The beta-functions for a homogeneous background are given perturbatively in terms of the data o f the original conformal theory without any specific assumptions on it s nature. The renormalization of couplings to primary operators and to first descendents is considered as well as that of couplings of a dil atonic type which involve explicit dependence on world sheet curvature . The first descendent couplings are interpreted as gauge degrees of f reedom in the string field action and the corresponding gauge transfor mation is spelled out.