Comments on BRST quantization of strings

TL;DR

This paper revisits the BRST quantization of strings, streamlining the derivation of scattering amplitude measures and incorporating zero mode gauge invariances using the Batalin-Vilkovisky formalism, with applications to bosonic string theory and topological gravity.

Contribution

It introduces a BRST-invariant gauge-fixed action including zero mode insertions and offers a novel approach to anomalous contributions in moduli space boundaries.

Findings

BRST-invariant gauge-fixed action with zero modes derived

Path integral measure for scattering amplitudes streamlined

Anomalous contributions to BRST Ward identities analyzed

Abstract

The BRST quantization of strings is revisited and the derivation of the path integral measure for scattering amplitudes is streamlined. Gauge invariances due to zero modes in the ghost sector are taken into account by using the Batalin-Vilkovisky formalism. This involves promoting the moduli of Riemann surfaces to quantum mechanical variables on which BRST transformations act. The familiar ghost and antighost zero mode insertions are recovered upon integrating out auxiliary fields. In contrast to the usual treatment, the gauge-fixed action including all zero mode insertions is BRST invariant. Possible anomalous contributions to BRST Ward identities due to boundaries of moduli space are reproduced in a novel way. Two models are discussed explicitly: bosonic string theory and topological gravity coupled to the topological A-model.