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

DOI10.1142/S0217732394002616zbMATH Open1021.81835arXivhep-th/9403062OpenAlexW2134692286MaRDI QIDQ2727894

Publication date: 31 July 2001

Published in: Modern Physics Letters A (Search for Journal in Brave)

Abstract: The one-loop effective potential in

2 D

dilaton gravity in conformal gauge on the topologically non-trivial plane

e a l s i m e s S^{1}

and on the hyperbolic plane

H^{2} / G a m m a

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} / G a m m a

). 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.

Full work available at URL: https://arxiv.org/abs/hep-th/9403062

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40)

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