High Energy Physics

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.

Resent research seems to indicate that charged extremal black holes in D=4 supersymmetric theories should be most naturally described in terms of more primitive atomic constituents. I will briefly describe what I mean by these atomic constituents and how they appear to play a role in both BPS and non-BPS extremal black holes.

It has been known for a long time that instanton effects control the large order behavior of the perturbation series in quantum mechanics and gauge theories. I present a study of this connection in the context of matrix models in 1/N-expansion and topological strings. I will show how to compute the one-instanton corrections for a generic matrix model. Due to a recent matrix model inspired formalism for the topological string amplitudes on local Calabi-Yau manifolds, this can be used to compute nonperturbative effects in topological string theory and make predictions about the asymptotics of the string perturbation series. I discuss various cases where our predictions can be tested, yielding spectacular agreement with the asymptotics extracted by standard numerical methods.

Some recent investigations into the structure of the AdS/CFT correspondence rely on input from increasingly complicated technical calculations. Two related examples in planar N=4 super Yang-Mills theory include testing consequences of integrability and exploring iteration relations amongst multiloop gluon scattering amplitudes. I will review the latest developments in these areas and the methods used to carry out relevant calculations through four loops.