Exact Path Integral Quantization of Generic 2-D Dilaton Gravity

TL;DR

The paper develops a local, nonperturbative path integral quantization of generic 2D dilaton gravity and shows that, in the absence of matter, the quantum effective action coincides with the classical action, solving apparent contradictions with Dirac quantization. Using a first-order Cartan formulation in an Eddington–Finkelstein–type gauge and a canonical BV-BRST framework, the authors prove equivalence to the second-order formulation and demonstrate that no local quantum corrections arise. They extend the analysis to the Jackiw–Teitelboim model with matter, where the Polyakov action is incorporated and the path integral can be carried out exactly, yielding a nonperturbative generating functional and showing local equivalence to the classical JT theory with the Polyakov term. The work highlights the robustness of local quantum effects in 2D dilaton gravity, clarifies UV properties, and discusses the importance of boundary terms and global aspects for a complete quantum treatment.

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.