Another View on Massless Matter-Gravity Fields in Two Dimensions

TL;DR

This paper explores an alternative quantization approach for two-dimensional matter-gravity theories that preserves Weyl invariance at the expense of diffeomorphism invariance, revealing a different gauge symmetry structure.

Contribution

It introduces a novel quantization method that maintains Weyl invariance by sacrificing diffeomorphism invariance, offering new insights into symmetry preservation in 2D gravity theories.

Findings

Weyl invariance can be preserved without diffeomorphism invariance.

The alternative approach retains a subset of coordinate redefinition invariances.

Both the conventional and alternative formulations possess comparable gauge symmetries.

Abstract

Conventional quantization of two-dimensional diffeomorphism and Weyl invariant theories sacrifices the latter symmetry to anomalies, while maintaining the former. When alternatively Weyl invariance is preserved by abandoning diffeomorphism invariance, we find that some invariance against coordinate redefinition remains: one can still perform at will transformations possessing a constant Jacobian. The alternate approach enjoys as much ``gauge'' symmetry as the conventional formulation.