  We perform a renormalization group analysis of some important effective field
theoretic models for deconfined spinons. We show that deconfined spinons are
critical for an isotropic SU(N) Heisenberg antiferromagnet, if $N$ is large
enough. We argue that nonperturbatively this result should persist down to N=2
and provide further evidence for the so called deconfined quantum criticality
scenario. Deconfined spinons are also shown to be critical for the case
describing a transition between quantum spin nematic and dimerized phases. On
the other hand, the deconfined quantum criticality scenario is shown to fail
for a class of easy-plane models. For the cases where deconfined quantum
criticality occurs, we calculate the critical exponent $\eta$ for the decay of
the two-spin correlation function to first-order in $\epsilon=4-d$. We also
note the scaling relation $\eta=d+2(1-\phi/\nu)$ connecting the exponent $\eta$
for the decay to the correlation length exponent $\nu$ and the crossover
exponent $\phi$.
