D=26 and Exact Solution to the Conformal-Gauge Two-Dimensional Quantum Gravity

TL;DR

This paper provides an exact solution to two-dimensional quantum gravity in the conformal gauge, highlighting the special case at D=26 where anomalies vanish, and clarifies misconceptions about ghost number anomalies.

Contribution

It offers a complete Heisenberg picture solution for conformal-gauge 2D quantum gravity and clarifies the nature of anomalies at D=26.

Findings

Explicit n-point Wightman functions obtained

Anomaly absence at D=26 confirmed

Ghost number current anomaly considered an illusion

Abstract

The conformal-gauge two-dimensional quantum gravity is formulated in the framework of the BRS quantization and solved completely in the Heisenberg picture: All n-point Wightman functions are explicitly obtained. The field-equation anomaly is shown to exist as in other gauges, but there is no other subtlety. At the critical dimension D=26 of the bosonic string, the field-equation anomaly is shown to be absent. However, this result is not equivalent to the statement that the conformal anomaly is proportional to D-26. The existence of the FP-ghost number current anomaly is seen to be an illusion.