RENORMALIZATION GROUP AND STRING LOOPS

Abstract

The fixed points of the 2-d renormalization group flow are known to correspond to the tree level string vacua. We analyze how the “renormalization group” (or “sigma model”) approach can be extended to the string loop level. The central role of the condition of renormalizability of the generating functional for string amplitudes with respect to both “local” and “modular” infinities is emphasized. Several one- and two-loop examples of renormalization are discussed. It is found that in order to ensure the renormalizability of the generating functional one is to use “extended” (e.g. Schottky-type) parametrizations of moduli spaces. An approach to a resummation of the string perturbative expansion based on operators of insertion of topological fixtures is suggested.