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 an 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.
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