  We establish that spin liquids described in terms of gapless fermionic
(Dirac) spinons and gapless U(1) gauge fluctuations can be stable in two
dimensions, at least when the physical SU(2) spin symmetry is generalized to
SU(N). Equivalently, we show that compact QED3 has a deconfined phase for a
large number of fermion fields, in the sense that monopole fluctuations can be
irrelevant at low energies. A precise characterization is provided by an
emergent global topological U(1) symmetry corresponding to the conservation of
gauge flux. Beginning with an SU(N) generalization of the S=1/2 square lattice
Heisenberg antiferromagnet, we consider the pi-flux spin liquid and, via a
systematic analysis of all operators, show that there are NO relevant
perturbations (in the renormalization group sense) about the large-N spin
liquid fixed point, which is thus a stable phase. We provide a further
illustration of this conclusion with an approximate renormalization group
calculation that treats the gapless fermions and the monopoles on an equal
footing. This approach directly points out some of the flaws in the erroneous
"screening" argument for the relevance of monopoles in compact QED3.
