  We discuss compact (2+1)-dimensional Maxwell electrodynamics coupled to
fermionic matter with N replica. For large enough N, the latter corresponds to
an effective theory for the nearest neighbor SU(N) Heisenberg antiferromagnet,
in which the fermions represent solitonic excitations known as spinons. Here we
show that the spinons are deconfined for $N>N_c=36$, thus leading to an
insulating state known as spin liquid. A previous analysis considerably
underestimated the value of $N_c$. We show further that for $20<N\leq 36$ there
can be either a confined or a deconfined phase, depending on the instanton
density. For $N\leq 20$ only the confined phase exist. For the physically
relevant value N=2 we argue that no paramagnetic phase can emerge, since chiral
symmetry breaking would disrupt it. In such a case a spin liquid or any other
nontrivial paramagnetic state (for instance, a valence-bond solid) is only
possible if doping or frustrating interactions are included.
