Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-04-21
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.
Elizalde Emilio
Naftulin S.
Odintsov Sergei D.
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