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Non-Trivial Ultraviolet Fixed Point in Quantum Gravity

The non-trivial ultraviolet fixed point in quantum gravity is calculated by means of the exact renormalization group equation in d-dimensions (2 � d ≤ 4). It is shown that the ultraviolet non-Gaussian fixed point which is expected from the perturbativelly �-expanded calculations in 2 + � gravity theory remains in d = 4. Hence it is possible that quantum gravity is an asymptotically safe theory and renormalizable in 2