Batalin-Vilkoviski master equation and absence of anomalies in string field theory

TL;DR

This paper investigates the Batalin-Vilkovisky master equation in string field theory, demonstrating anomaly absence in open strings with closed string coupling and discussing perturbative solutions in closed strings.

Contribution

It provides a detailed analysis of anomaly cancellation in string field theory using the BV formalism and explores perturbative solutions for closed string cases.

Findings

Open string theory is anomaly free with closed string coupling.

Perturbative solutions exist for the closed string master equation.

Discussion on non-perturbative corrections and formal methods.

Abstract

We study the Batalin-Vilkovisky master equation for both open and closed string field theory with special attention to anomalies. Open string field theory is anomaly free once the minimal coupling to closed strings induced by loop amplitudes is considered. In closed string field theory the full-fledged master equation has to be solved order by order in perturbation theory. The existence of a solution implies the absence of anomaly. We briefly discuss the relation of the iterative process of solution to methods used in the first quantized formalism and comment on some possible non-perturbative corrections.