Exact Path Integral Quantization of Generic 2-D Dilaton Gravity

TL;DR

This paper proves that for generic 2D dilaton gravity without matter, the quantum effective action matches the classical action to all orders, resolving discrepancies between different quantization methods.

Contribution

It demonstrates that the local path integral quantization yields no quantum corrections for 2D dilaton gravity without matter, aligning with Dirac quantization results.

Findings

Quantum effective action equals classical action in absence of matter.

Results extend to Jackiw--Teitelboim model with matter.

Resolves contradiction between Dirac and path-integral quantizations.

Abstract

Local path integral quantization of generic 2D dilaton gravity is considered. Locality means that we assume asymptotic fall off conditions for all fields. We demonstrate that in the absence of `matter' fields to all orders of perturbation theory and for all 2D dilaton theories the quantum effective action coincides with the classical one. This resolves the apparent contradiction between the well established results of Dirac quantization and perturbative (path-integral) approaches which seemed to yield non-trivial quantum corrections. For a particular case, the Jackiw--Teitelboim model, our result is even extended to the situation when a matter field is present.