  Unimodular gravity is classically equivalent to standard Einstein gravity,
but differs when it comes to the quantum theory: The conformal factor is
non-dynamical, and the gauge symmetry consists of transverse diffeomorphisms
only. Furthermore, the cosmological constant is not renormalized. Thus the
quantum theory is distinct from a quantization of standard Einstein gravity.
Here we show that within a truncation of the full Renormalization Group flow of
unimodular quantum gravity, there is a non-trivial ultraviolet-attractive fixed
point, yielding a UV completion for unimodular gravity. We discuss important
differences to the standard asymptotic-safety scenario for gravity, and provide
further evidence for this scenario by investigating a new form of the
gauge-fixing and ghost sector.
