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

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

1992-08-04

arxiv.org/abs/hep-th/9208015v1

Phys.Rev. D46 (1992) 5449-5457

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, OKHEP 92-001

Scientific paper

10.1103/PhysRevD.46.5449

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 ($c \phi R$), and self interacting by an arbitrary potential term $V(\phi)$. 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.

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