Renormalization Group and String Loops

TL;DR

This paper explores extending the renormalization group approach to string theory beyond tree level, analyzing one- and two-loop renormalization, and proposing methods for resumming string perturbation series.

Contribution

It introduces an extended parametrization of moduli space and a resummation approach for string perturbation expansion at loop levels.

Findings

Renormalizability requires an extended moduli space parametrization.

One-loop and two-loop renormalization examples are provided.

A resummation method using topological fixtures is proposed.

Abstract

Fixed points of the 2d renormalization group flow are known to correspond to tree level string vacua. We discuss 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-loop and two-loop examples of renormalization are considered. It is found that in order to ensure the renormalizability of the generating functional one is to use an "extended" (Schottky-type) parametrization of the moduli space. An approach to resummation of the string perturbative expansion based on operators of insertion of topological fixtures is suggested.