  We describe the phase diagram of electrons on a fully connected lattice with
random hopping, subject to a random Heisenberg spin exchange interactions
between any pair of sites and a constraint of no double occupancy. A
perturbative renormalization group analysis yields a critical point with
fractionalized excitations at a non-zero critical value $p_c$ of the hole
doping $p$ away from the half-filled insulator. We compute the renormalization
group to two loops, but some exponents are obtained to all loop order. We argue
that the critical point $p_c$ is flanked by confining phases: a disordered
Fermi liquid with carrier density $1+p$ for $p>p_c$, and a metallic spin glass
with carrier density $p$ for $p<p_c$. Additional evidence for the critical
behavior is obtained from a large $M$ analysis of a model which extends the
SU(2) spin symmetry to SU($M$). We discuss the relationship of the vicinity of
this deconfined quantum critical point to key aspects of cuprate phenomenology.
