The effect of coupling non-compact fi(I) gauge fields to four dimensio
nal simplicial quantum gravity is studied using strong coupling expans
ions and Monte Carlo simulations. For one gauge field the back-reactio
n of the matter on the geometry is weak. This changes, however, as mor
e matter fields are introduced. For more than two gauge fields the deg
eneracy of random manifolds Into branched polymers does not occur. and
the branched polymer phase seems to be replaced by a new phase with a
negative string susceptibility exponent gamma and fractal dimension d
(H) approximate to 4. (C) 1998 Elsevier Science B.V.