One-loop effective potential in 2D dilaton gravity on hyperbolic plane

Details One-loop effective potential in 2D dilaton gravity on hyperbolic plane One-loop effective potential in 2D dilaton gravity on hyperbolic plane

1994-03-10

arxiv.org/abs/hep-th/9403062v1

Mod.Phys.Lett.A9:2761-2766,1994

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, LaTex, UB-ECM-PF 94/3

Scientific paper

10.1142/S0217732394002616

The one-loop effective potential in $2D$ dilaton gravity in conformal gauge on the topologically non-trivial plane $\reals \times S^1$ and on the hyperbolic plane $H^2/\Gamma$ is calculated. For arbitrary choice of the tree scalar potential it is shown, that the one-loop effective potential explicitly depends on the reference metric (through the dependence on the radius of the torus or the radius of $H^2/\Gamma$). This phenomenon is absent only for some special choice of the tree scalar potential corresponding to the Liouville potential and leading to one-loop ultraviolet finite theory. The effective equations are discussed and some interpretation of the reference metric dependence of the effective potential is made.

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