Constrained BV Description of String Field Theory

TL;DR

This paper introduces a simplified constrained BV framework for string field theory, enabling a more straightforward description of open superstring field theory while maintaining equivalence with traditional methods.

Contribution

A new constrained BV approach for string field theory that simplifies the description of open superstring field theory and aligns with classical WZW-like actions.

Findings

Equivalent to conventional BV for bosonic strings

Simplifies BV description for open superstrings

Allows WZW-like form of BV action

Abstract

In the conventional BV description of string field theory, the string field Phi is split as Phi = Psi+Psi* where Psi includes all states with ghost number less than or equal to G and describes the spacetime fields, and Psi* includes all states with ghost number >G and describes the spacetime antifields. A new approach is proposed here in which separate string fields Psi and Psi* of unrestricted ghost number describe the spacetime fields and antifields. The string antifield Psi* is constrained to satisfy Psi* = {\partial L}/{\partial(Q Psi)} where L is the BV Lagrangian and Q is the worldsheet BRST operator. Dirac antibrackets are defined using this constraint, and the resulting description is equivalent to the conventional BV description for open and closed bosonic string field theory. For open superstring field theory, this constrained BV description is much simpler than the conventional BV description and allows the BV action to be expressed in the same WZW-like form as the classical action.