H. Dorn, ON GRAVITATIONAL DRESSING OF RENORMALIZATION-GROUP BETA-FUNCTIONS BEYOND LOWEST ORDER OF PERTURBATION-THEORY, Physics letters. Section B, 343(1-4), 1995, pp. 81-86
Based on considerations in conformal gauge I derive up to nextleading
order a relation between the coefficients of beta-functions in 2D reno
rmalizable field theories before and after coupling to quantized gravi
ty. The result implies a coupling constant dependence of the ratio of
both beta-functions beyond leading order.