  Recently Hermele et. al claimed that the infrared (IR) fixed point of
non-compact $QED_3$ is stable against instanton excitations in the limit of
large flavors of massless Dirac fermions [cond-mat/0404751]. We investigate an
effect of non-magnetic disorder on the deconfined quantum critical phase dubbed
U(1) spin liquid ($U1SL$) in the context of quantum antiferromagnet. In the
case of weak disorder the IR fixed point remains stable against the presence of
both the instanton excitations and non-magnetic disorder and thus the $U1SL$ is
sustained. In the case of strong disorder the IR fixed point becomes unstable
against the disorder and the Anderson localization is expected to occur. We
argue that in this case deconfinement of spinons does not occur since the Dirac
fermion becomes massive owing to the localization.
