Renormalization Group Flow in BRST Invariant Open String $\sigma$-Model

TL;DR

This paper explores the renormalization group flow in a BRST invariant open string sigma-model, revealing how interactions break BRST symmetry and generate non-linear gauge symmetries, connecting to Witten's string field theory.

Contribution

It demonstrates the non-perturbative effective action and gauge symmetry properties derived from beta-functions, linking sigma-model interactions to Witten's string field theory structure.

Findings

Explicit breaking of BRST invariance by interactions

Generation of non-linear gauge symmetries

Reproduction of Witten's vertex couplings in Feynman-Siegel gauge

Abstract

The renormalization group flow in the theory space of a BRST invariant string $\sigma$-model is investigated. For the open bosonic string the non-perturbative off-shell effective action and its gauge symmetry properties are determined from $\beta$-functions defined by the local Weyl anomaly. The interactions are shown to explicitly break the free theory BRST invariance generating new non-linear gauge symmetries of the type present in Witten's string field theory. In the Feynman-Siegel gauge the $\sigma$-model is shown to generate Witten's structure of vertex couplings.