Star Democracy in Open String Field Theory

TL;DR

This paper investigates the relationships between different star products in open string field theory, revealing compact relations among their Neumann coefficients and confirming the equivalence of certain ghost and matter sectors.

Contribution

It explicitly demonstrates the relations between ghost, twisted ghost, and matter Neumann coefficients, including the Gross-Jevicki relation, and proves the equivalence of matter and twisted ghost coefficients.

Findings

Neumann coefficients of ghost, twisted ghost, and matter sectors are related compactly.

Matter and twisted ghost coefficients differ only by a minus sign.

Spectrum of twisted ghost vertices matches conformal field theory predictions.

Abstract

We study three types of star products in SFT: the ghosts, the twisted ghosts and the matter. We find that their Neumann coefficients are related to each other in a compact way which includes the Gross-Jevicki relation between matter and ghost sector: we explicitly show that the same relation, with a minus sign, holds for the twisted and nontwisted ghost (which are different but define the same solution). In agreement with this, we prove that matter and twisted ghost coefficients just differ by a minus sign. As a consistency check, we also compute the spectrum of the twisted ghost vertices from conformal field theory and, using equality of twisted and reduced slivers, we derive the spectrum of the non twisted ghost star.