  4D Einstein gravity coupled to scalars and abelian gauge fields in its
2-Killing vector reduction is shown to be quasi-renormalizable to all loop
orders at the expense of introducing infinitely many essential couplings. The
latter can be combined into one or two functions of the `area radius'
associated with the two Killing vectors. The renormalization flow of these
couplings is governed by beta functionals expressible in closed form in terms
of the (one coupling) beta function of a symmetric space sigma-model.
Generically the matter coupled systems are asymptotically safe, that is the
flow possesses a non-trivial UV stable fixed point at which the trace anomaly
vanishes. The main exception is a minimal coupling of 4D Einstein gravity to
massless free scalars, in which case the scalars decouple from gravity at the
fixed point.
