Two-loop prediction for scaling exponents in (2 + ∈)-dimensional quantum gravity

We perform the two-loop level renormalization of quantum gravity in 2 + ∈ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly show that the theory is renormalizable to the two-loop level in our formalism. We further make a physical prediction for the scaling relation between the gravitational coupling constant and the cosmological constant which is expected to hold at the short distance fixed point of the renormalization group. It is found that the two-loop level calculation is necessary to determine the scaling exponent to the leading order in ∈.