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

TL;DR

This paper investigates anomalies in a simple model analogous to lightcone-gauge 2D quantum gravity, revealing that certain field equation breakdowns are due to gauge choices, and demonstrates how a transformation can eliminate these anomalies.

Contribution

It shows that anomalies observed in complex 2D quantum gravity models also appear in a simplified model, and identifies the transformation that removes these anomalies.

Findings

Anomalies occur in a simple analogous model of 2D quantum gravity.

A nonsingular transformation can convert the model into a free field theory without anomalies.

The cause of the anomaly discrepancy is analyzed and explained.

Abstract

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.