We extend recent results on scalar–tensor theories to the case of an O ( N ) -invariant multiplet. Some exact fixed point solutions of the RG flow equations are discussed. We find that also in the functional context, on employing a standard “type-I” cutoff, too many scalars destroy the gravitational fixed point. For d = 3 we show the existence of the gravitationally dressed Wilson–Fisher fixed point also for N 1 . We discuss also the results of the analysis for a different, scalar-free, coarse-graining scheme.
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