Exact Path Integral Quantization of 2-D Dilaton Gravity

TL;DR

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

Contribution

It establishes an exact path integral quantization result for 2D dilaton gravity, showing no quantum corrections in the effective action when matter is absent.

Findings

Quantum effective action equals classical action in matter-free 2D dilaton gravity

Results extend to the JT model with matter fields present

Clarifies the relationship between Dirac and path-integral quantization methods

Abstract

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 the Jackiw--Teitelboim (JT) model, our result is even extended to the situation when a matter field is present.