All-Order Quantum Gravity in Two Dimensions

Abstract

We derive curvature counterterms in two-dimensional gravity coupled to conformal matter up to infinite order. By construction the higher-order action is equivalent to a finite first-order theory with auxiliary scalar. Due to this equivalence it shares the following remarkable properties: There is no need for gravitational dressing of the cosmological constant, quantization is consistent for any conformal anomaly $c$ of the coupled matter system, and if the coupled matter system is a $c=d$-dimensional string theory in a Euclidean background then the effective string theory is $D=d+2$-dimensional with Minkowski signature $(1,D-1)$. The resulting quantum theory favours flat geometries and suppresses both parabolic and hyperbolic singularities.

22 pages (phyzzx.tex, figures available by mail upon request), SLAC-PUB 6274 T

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Cited by in corpus (4)

• Exact Solution of Discrete Two-Dimensional R^2 Gravity
• On Higher Derivative Gravity in Two Dimensions
• Classical Solution of Two Dimensional $R^2$-Gravity and Cross-Over Phenomenon
• The Quantization of Anomalous Gauge Field Theory and BRST-invariant Models of Two Dimensional Quantum Gravity