The Renormalization Structure and Quantum Equivalence of 2D Dilaton Gravities

TL;DR

This paper derives the one-loop effective action for a general 2D dilaton gravity model, investigates quantum equivalence of classically equivalent models, and analyzes their renormalization group flows, revealing that some models are not fixed points.

Contribution

It provides explicit calculations of the effective action and renormalization group equations for general 2D dilaton gravities, demonstrating quantum equivalence on-shell and analyzing specific models.

Findings

Classically equivalent dilaton gravities are perturbatively equivalent on-shell.

The effective action and RG equations are explicitly derived for general models.

The CGHS model is shown not to be a fixed point of the RG flow.

Abstract

The one-loop effective action corresponding the general model of dilaton gravity given by the Lagrangian $L=-\sqrt{g} \left[ \frac{1}{2}Z(\Phi ) g^{\mu\nu} \partial_\mu \Phi \partial_\nu \Phi + C(\Phi ) R + V (\Phi )\right]$, where $Z(\Phi )$, $ C(\Phi )$ and $V (\Phi )$ are arbitrary functions of the dilaton field, is found. The question of the quantum equivalence of classically equivalent dilaton gravities is studied. By specific calculation of explicit examples it is shown that classically equivalent quantum gravities are also perturbatively equivalent at the quantum level, but only on-shell. The renormalization group equations for the generalized effective couplings $Z(\Phi )$, $ C(\Phi )$ and $V (\Phi )$ are written. An analysis of the equations shows, in particular, that the Callan-Giddings-Harvey-Strominger model is not a fixed point of these equations.