We construct a consistent closure for the beta functions of the cosmological and Newton's constants by evaluating the influence that the anomalous dimensions of the fluctuating metric and ghost fields have on their renormalization group flow. In this generalized framework we confirm the presence of a UV attractive non-Gaussian fixed point, which we find characterized by real critical exponents. Our closure method is general and can be applied systematically to more general truncations of the gravitational effective average action.
We compute critical exponents of O(N )-models in fractional dimensions between two and four, and for continuos values of the number of field components N , in this way completing the RG classification of universality classes for these models. In d = 2 the N -dependence of the correlation length critical exponent gives us the last piece of information needed to establish a RG derivation of the Mermin-Wagner theorem. We also report critical exponents for multi-critical universality classes in the cases N ≥ 2 and N = 0. Finally, in the large-N limit our critical exponents correctly approach those of the spherical model, allowing us to set N ∼ 100 as threshold for the quantitative validity of leading order large-N estimates.
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