On Ghost Structure of Vacuum Superstring Field Theory

TL;DR

This paper investigates the ghost structure of vacuum superstring field theory, deriving a twist-invariant kinetic operator with sector-dependent action, and constructs a solution related to a non-BPS D9-brane.

Contribution

It introduces a novel twist-invariant pure-ghost kinetic operator with sector-dependent action, crucial for gauge invariance, and constructs a related non-BPS D-brane solution.

Findings

Derived a twist-invariant kinetic operator Q^ with sector-dependent action.

Showed the importance of this structure for gauge invariance.

Constructed a solution corresponding to a non-BPS D9-brane.

Abstract

After discussing the general form of the kinetic operator around the tachyon vacuum, we determine the specific form of the pure-ghost kinetic operator Q^ by requiring the twist invariance of the action. We obtain a novel result that the Grassmann-even piece Q_even of Q^ must act differently on GSO(+) sector and on GSO(-) sector to preserve the twist invariance, and show that this structure is crucial for gauge invariance of the action. With this choice of Q^, we construct a solution in an approximation scheme which is conjectured to correspond to a non-BPS D9-brane. We consider both 0-picture cubic and Berkovits' non-polynomial superstring field theories for the NS sector.