  Many popular models of fractionalized spin liquids contain neutral fermionic
spinon excitations on a Fermi surface, carrying unit charges under a compact
U(1) gauge force. We argue that instanton effects generically render such
states unstable to confinement in two spatial dimensions, so that all
elementary excitations are gauge neutral, and there is no spinon Fermi surface.
Similar results are expected to apply to SU(2) spin liquids. However,
fractionalized states can appear when the gauge symmetry is broken down to a
discrete subgroup by the Higgs mechanism. Our argument generalizes earlier
results on confinement in the pure gauge theory, and on the instability of the
U(1) staggered flux and algebraic spin liquids with a Dirac spectrum for
fermionic spinons.
