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

Klaus Kirsten·Sergei Odintsov
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Abstract

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 $H^2/Γ$ 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 $H^2/Γ$). 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.

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Klaus Kirsten, Sergei Odintsov. 1994-03-10. One-loop effective potential in 2D dilaton gravity on hyperbolic plane. https://doi.org/10.1142/s0217732394002616

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