ON THE RENORMALIZATION GROUP APPROACH TO STRING EQUATIONS OF MOTION

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Abstract
We discuss the program of deriving the string field theory equations of motion for all (massless and massive) string modes as the renormalization group fixed point equations for the most general sigma model containing all possible ("nonrenormalizable") interactions. We review the approach based on the Wilson RG equation and point out the problem of cutoff dependence of the interaction term in the corresponding "quadratic" beta function. The relation between the sigma model path integral and the string scattering amplitudes is clarified. We suggest a new approach to the derivation of the generalized sigma model beta functions in which the central role is played by the condition of completeness of the set of interaction terms ("vertex opeators") present in the sigma model action. The use of the completeness relation makes it possible to obtain closed expressions for the sigma model partition function and the beta functions. The resulting beta functions contain all higher powers of the couplings (fields).

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