Construction of an Identically Nilpotent BRS Charge in the Kato-Ogawa String Theory

TL;DR

This paper extends previous results on 2D quantum gravity in BRS formalism to finite-length bosonic strings, constructing a nilpotent BRS charge for the Kato-Ogawa string theory and clarifying ghost vacuum structure.

Contribution

It explicitly constructs a nilpotent BRS charge for finite-length bosonic strings, including the Kato-Ogawa case, avoiding indefinite metrics and clarifying ghost vacuum structure.

Findings

BRS charge is nilpotent even for D≠26.

The field-equation anomaly persists in finite-string cases.

Ghost vacuum structure is clarified without artificial indefinite metrics.

Abstract

In previous work, the conformal-gauge two-dimensional quantum gravity in the BRS formalism has been solved completely in terms of Wightman functions. In the present paper, this result is extended to the closed and open bosonic strings of finite length; the open-string case is nothing but the Kato-Ogawa string theory. The field-equation anomaly found previously, which means a slight violation of a field equation at the level of Wightman functions, remains existent also in the finite-string cases. By using this fact, a BRS charge nilpotent even for $D\not=26$ is explicitly constructed in the framework of the Kato-Ogawa string theory. The FP-ghost vacuum structure of the Kato-Ogawa theory is made more transparent; the appearance of half-integral ghost numbers and the artificial introduction of indefinite metric are avoided.