  We describe spin correlations in the vicinity of a generalized impurity in a
wide class of fractionalized spin liquid states. We argue that the primary
characterization of the impurity is its electric charge under the gauge field
describing singlet excitations in the spin liquid. We focus on two gapless U(1)
spin liquids described by 2+1 dimensional conformal field theories (CFT): the
staggered flux (sF) spin liquid, and the deconfined critical point between the
Neel and valence-bond-solid (VBS) states. In these cases, the electric charge
is argued to be an exactly marginal perturbation of the CFT. Consequently, the
impurity susceptibility has a 1/T temperature dependence, with an anomalous
Curie constant which is a universal number associated with the CFT. One
unexpected feature of the CFT of the sF state is that an applied magnetic field
does not induce any staggered spin polarization in the vicinity of the impurity
(while such a staggered magnetization is present for the Neel-VBS case). These
results differ significantly from earlier theories of vacancies in the sF
state, and we explicitly demonstrate how our gauge theory corrects these works.
We discuss implications of our results for the cuprate superconductors and
organic Mott insulators.
