  We present a general hydrodynamic theory of transport in the vicinity of
superfluid-insulator transitions in two spatial dimensions described by
"Lorentz"-invariant quantum critical points. We allow for a weak impurity
scattering rate, a magnetic field B, and a deviation in the density, \rho, from
that of the insulator. We show that the frequency-dependent thermal and
electric linear response functions, including the Nernst coefficient, are fully
determined by a single transport coefficient (a universal electrical
conductivity), the impurity scattering rate, and a few thermodynamic state
variables. With reasonable estimates for the parameters, our results predict a
magnetic field and temperature dependence of the Nernst signal which resembles
measurements in the cuprates, including the overall magnitude. Our theory
predicts a "hydrodynamic cyclotron mode" which could be observable in ultrapure
samples. We also present exact results for the zero frequency transport
co-efficients of a supersymmetric conformal field theory (CFT), which is
solvable by the AdS/CFT correspondence. This correspondence maps the \rho and B
perturbations of the 2+1 dimensional CFT to electric and magnetic charges of a
black hole in the 3+1 dimensional anti-de Sitter space. These exact results are
found to be in full agreement with the general predictions of our hydrodynamic
analysis in the appropriate limiting regime. The mapping of the hydrodynamic
and AdS/CFT results under particle-vortex duality is also described.
