On the BV formalism of open superstring field theory in the large Hilbert space

TL;DR

This paper develops BV master actions for open superstring field theory in the large Hilbert space, addressing breakdowns of conventional approaches and proposing reassembly methods based on Berkovits' constrained BV framework.

Contribution

It introduces a novel reassembly of string fields-antifields for BV formalism in the large Hilbert space, overcoming previous limitations and connecting theories in different Hilbert spaces.

Findings

Conventional BV approach breaks down at third antifield order in large Hilbert space.

A reassembly method based on Berkovits' constrained BV approach is proposed.

Constructed a BV master action using a minimal set of string fields-antifields.

Abstract

We construct several BV master actions for open superstring field theory in the large Hilbert space. First, we show that a naive use of the conventional BV approach breaks down at the third order of the antifield number expansion, although it enables us to define a simple "string antibracket" taking the Darboux form as space-time antibrackets. This fact implies that in the large Hilbert space, "string fields-antifields" should be reassembled to obtain master actions in a simple manner. We determine the assembly of the string antifields on the basis of Berkovits' constrained BV approach, and give solutions to the master equation defined by Dirac antibrackets on the constrained string field-antifield space. It is expected that partially gauge-fixing enables us to relate superstring field theories based on the large and small Hilbert spaces directly: Reassembling string fields-antifields is rather natural from this point of view. Finally, inspired by these results, we revisit the conventional BV approach and construct a BV master action based on the minimal set of string fields-antifields.