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We present a general hydrodynamic theory of transport in the vicinity ofsuperfluid-insulator transitions in two spatial dimensions described by"Lorentz"-invariant quantum critical points. We allow for a weak impurityscattering rate, a magnetic field B, and a deviation in the density, \rho, fromthat of the insulator. We show that the frequency-dependent thermal andelectric linear response functions, including the Nernst coefficient, are fullydetermined by a single transport coefficient (a universal electricalconductivity), the impurity scattering rate, and a few thermodynamic statevariables. With reasonable estimates for the parameters, our results predict amagnetic field and temperature dependence of the Nernst signal which resemblesmeasurements in the cuprates, including the overall magnitude. Our theorypredicts a "hydrodynamic cyclotron mode" which could be observable in ultrapuresamples. We also present exact results for the zero frequency transportco-efficients of a supersymmetric conformal field theory (CFT), which issolvable by the AdS/CFT correspondence. This correspondence maps the \rho and Bperturbations of the 2+1 dimensional CFT to electric and magnetic charges of ablack hole in the 3+1 dimensional anti-de Sitter space. These exact results arefound to be in full agreement with the general predictions of our hydrodynamicanalysis in the appropriate limiting regime. The mapping of the hydrodynamicand AdS/CFT results under particle-vortex duality is also described.

Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes