Physical Degrees of Freedom in 2-D String Field Theories

TL;DR

This paper investigates the role of certain cohomology states in 2-D string field theories, revealing their auxiliary nature and importance in symmetry identities, while analyzing ghost structures in specific gauges.

Contribution

It clarifies the nature of absolute and semi-relative cohomology states and their impact on the string field theory action and symmetry equations.

Findings

States outside relative cohomology are auxiliary fields without kinetic terms.

Absolute cohomology states are lost in the Siegel gauge.

These states are crucial for the master equation of Ward-Takahashi identities.

Abstract

States in the absolute (semi-relative) cohomology but not in the relative cohomology are examined through the component decomposition of the string field theory action for the 2-D string. It is found that they are auxiliary fields without kinetic terms, but are important for instance in the master equation for the Ward-Takahashi identities. The ghost structure is analyzed in the Siegel gauge, but it is noted that the absolute (semi-relative) cohomology states are lost.