Regularizing Cubic Open Neveu-Schwarz String Field Theory

TL;DR

This paper introduces a new regularization method for cubic open Neveu-Schwarz string field theory using an operator N_ ho, which simplifies the linearized equations of motion and avoids the need for Hilbert space truncation.

Contribution

It proposes replacing the midpoint insertion Yar Y with an invertible operator N_ ho depending on a parameter, simplifying the linearized equations of motion in the theory.

Findings

N_ ho operator is invertible and equals 1 up to a BRST-trivial term

Linearized equation N_ ho QV=0 implies QV=0 without truncation

Provides a regularization scheme for string field theory equations

Abstract

After introducing non-minimal variables, the midpoint insertion of Y\bar Y in cubic open Neveu-Schwarz string field theory can be replaced with an operator N_\rho depending on a constant parameter \rho. As in cubic open superstring field theory using the pure spinor formalism, the operator N_\rho is invertible and is equal to 1 up to a BRST-trivial quantity. So unlike the linearized equation of motion Y\bar Y QV=0 which requires truncation of the Hilbert space in order to imply QV=0, the linearized equation N_\rho QV=0 directly implies QV=0.