Is Quantum Einstein Gravity Nonperturbatively Renormalizable?

Abstract

We find considerable evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity is ``asymptotically safe'' in Weinberg's sense. This would mean that the theory is likely to be nonperturbatively renormalizable and thus could be considered a fundamental (rather than merely effective) theory which is mathematically consistent and predictive down to arbitrarily small length scales. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The truncation ansatz includes the Einstein-Hilbert action and a higher derivative term.

18 pages, latex, 3 figures

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• Exact evolution equation for the effective potential
• Nonperturbative renomalization group for Einstein gravity with matter
• Gauge invariance, background fields and modified Ward identities

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