All Symmetries of Non-Einsteinian Gravity in $d =2$

TL;DR

This paper thoroughly analyzes the symmetries of two-dimensional $R^2$-gravity with torsion, establishing gauge choices, symmetry correspondences, and anomaly absence, thus paving the way for consistent quantization.

Contribution

It provides a detailed covariant and Hamiltonian analysis of 2D $R^2$-gravity with torsion, clarifying its gauge symmetries and confirming anomaly-free quantization.

Findings

Light-cone gauge is suitable for the model.

Hamiltonian gauge symmetries correspond to diffeomorphisms and Lorentz transformations.

The constraint algebra is anomaly-free, supporting Dirac quantization.

Abstract

The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the Hamiltonian gauge symmetries and the diffeomorphisms and local Lorentz transformations is established, thus proving that there are no hidden local symmetries responsible for the complete integrability of the model. Finally the constraint algebra is shown to have no quantum anomalies so that Dirac's quantization should be applicable.