One-loop Vilkovisky-DeWitt Counterterms for 2D Gravity plus Scalar Field Theory

Abstract

The divergent part of the one-loop off-shell effective action is computed for a single scalar field coupled to the Ricci curvature of 2D gravity ($c\varphi R$), and self interacting by an arbitrary potential term $V(\varphi )$. The Vilkovisky-DeWitt effective action is used to compute gauge-fixing independent results. In our background field/covariant gauge we find that the Liouville theory is finite on shell. Off-shell, we find a large class of renormalizable potentials which include the Liouville potential. We also find that for backgrounds satisfying $R=0$, the Liouville theory is finite off shell, as well.

19 pages, OKHEP 92-001

References in corpus (1)

• Scalar-Tensor Quantum Gravity in Two Dimensions

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