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 φ R), and self interacting by an arbitrary potential term V(φ). 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.