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

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.Comment: 23 pages, LaTe

Proof of the Gauge Independence of the Conformal Anomaly of Bosonic String in the Sense of Kraemmer and Rebhan

Kraemmer and Rebhan claimed the gauge independence of the conformal anomaly of bosonic string for various gauge fixings in the framework of the perturbation theory of two-dimensional quantum gravity. It is pointed out that their proof is wrong. The gauge independence is proved for the gauge-fixings which reduce to the linearized de Donder gauge in the flat limit of the background metric. Similar remarks are made also for the Rebhan-Kraemmer current anomaly.Comment: 14 pages, LaTeX, two stylefiles include

Anomaly Problem in a Simple Model Analogous to the Lightcone-Gauge Two-Dimensional Quantum Gravity

It was found in the two-dimensional quantum gravity both in the de Donder gauge and in the lightcone gauge that one of field equations breaks down at the level of the representation, though the breakdown is very little. It is shown that this anomalous behavior occurs also in a very simple model analogous to the lightcone-gauge two-dimensional quantum gravity. This model, however, can be transformed into a free field theory by a nonsingular transformation. Of course, the latter has no anomaly. The cause of the discrepancy is analyzed.Comment: 16 pages, LaTeX, overcite.st

Perturbative or Path-Integral Approach versus Operator-Formalism Approach

In the conformal-gauge two-dimensional quantum gravity, the solution obtained by the perturbative or path-integral approach is compared with the one obtained by the operator-formalism approach. Treatments of the anomaly problem in both approaches are different. This difference is found to be essentially caused by the fact that the perturbative or path-integral approach is based on the T*-product (covariantized T-product), which generally violates field equations. Indeed, this fact induces some extra one-loop Feynman diagrams, which would not exist unless a nonzero contribution arose from a zero field. Some demerits of the path-integral approach are explicitly demonstrated.Comment: 16 pages, PTPTe