  We write new functional renormalization group equations for a scalar
nonminimally coupled to gravity. Thanks to the choice of the parametrization
and of the gauge fixing they are simpler than older equations and avoid some of
the difficulties that were previously present. In three dimensions these
equations admit, at least for sufficiently small fields, a solution that may be
interpreted as a gravitationally dressed Wilson-Fisher fixed point. We also
find for any dimension d>2 two analytic scaling solutions which we study for
d=3 and d=4. One of them corresponds to the fixed point of the Einstein-Hilbert
truncation, the others involve a nonvanishing minimal coupling.

High Energy Physics - Theory