All-Order Quantum Gravity in Two Dimensions

TL;DR

This paper develops an all-order quantum gravity framework in two dimensions, showing it is equivalent to a finite first-order theory, and explores its implications for string theory and geometry.

Contribution

It introduces a novel all-order quantum gravity approach in 2D that simplifies to a finite first-order theory with auxiliary scalar fields, revealing new properties.

Findings

No need for gravitational dressing of the cosmological constant.

Quantization is consistent for any conformal anomaly c.

Favors flat geometries and suppresses certain singularities.

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.