The Renormalization Structure and Quantum Equivalence of 2D Dilaton Gravities

Details The Renormalization Structure and Quantum Equivalence of 2D Dilaton Gravities The Renormalization Structure and Quantum Equivalence of 2D Dilaton Gravities

1993-04-21

arxiv.org/abs/hep-th/9304091v1

Int.J.Mod.Phys.A9:933-952,1994

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, LaTeX file, April 21

Scientific paper

10.1142/S0217751X9400042X

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.

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