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

The one-loop effective potential in 2D dilaton gravity in conformal gauge on the topologically non-trivial plane IR×S and on the hyperbolic plane H/Γ 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/Γ). 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. E-mail: [email protected]. Alexander von Humboldt Foundation Fellow. E-mail: [email protected]. On leave from: Tomsk Pedagogical Institute, 634041 Tomsk, Russian Federation.