Anomaly In 2d-Gravity Coupled To Matter Fields

TL;DR

This paper discusses the challenges in defining a consistent quantum theory of 2D gravity coupled with matter fields due to anomalies in the constraints, highlighting fundamental issues in quantum gravity in lower dimensions.

Contribution

It identifies and analyzes the anomaly preventing the imposition of the Wheeler-DeWitt equation and the semiclassical WKB local time in 2D gravity with matter.

Findings

Anomaly obstructs the Wheeler-DeWitt equation in 2D gravity.

Anomaly prevents a semiclassical WKB local time.

Highlights fundamental issues in quantum gravity in 2D models.

Abstract

In 1+1 dimensions, the Wheeler-DeWitt equation cannot be imposed owing to an anomaly in its commutator with the diffeomorphism constraint. A similar obstruction prevents also a semiclassical definition of a WKB local time. (Talk given at the 7th Marcel Grossman Meeting on General Relativity, Stanford, July 28, 1994.)