Developing the Covariant Batalin-Vilkovisky approach to String Theory

TL;DR

This paper extends the covariant Batalin-Vilkovisky formalism to string theory, showing how different moduli space decompositions relate through canonical transformations and emphasizing the role of measures in background independence.

Contribution

It develops the BV approach for string field theory, explicitly deriving generators of field transformations and analyzing the impact of moduli space decompositions on gauge fixing.

Findings

Different moduli space decompositions lead to equivalent gauge-fixed actions

Field transformations are canonical with respect to the BV antibracket

Measures are crucial for background independence in quantum string field theory

Abstract

We investigate the variation of the string field action under changes of the string field vertices giving rise to different decompositions of the moduli spaces of Riemann surfaces. We establish that any such change in the string action arises from a field transformation canonical with respect to the Batalin-Vilkovisky (BV) antibracket, and find the explicit form of the generator of the infinitesimal transformations. Two theories using different decompositions of moduli space are shown to yield the same gauge fixed action upon use of different gauge fixing conditions. We also elaborate on recent work on the covariant BV formalism, and emphasize the necessity of a measure in the space of two dimensional field theories in order to extend a recent analysis of background independence to quantum string field theory.