This series consists of talks in the area of Superstring Theory.
I will present a construction of supersymmetric Wilson loop operators in N=4 SYM for an arbitrary path on an S3 subspace of space-time. I will show how they are evaluated in AdS and in particular that the string world-sheet is a generalized calibration with respect to an almost-complex structure associate to the supersymmetries preserved by the loop. I will present some special examples and in the case when the loop is restricted to an S2, some evidence that the calculation reduces to a perturbative calculation in YM in 2-dimensions on S2.
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.
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'll discuss a reformulation of twistor-string theory as a heterotic string. This clarifies why conformal supergravity arises and provides a link between the Berkovits and Witten pictures. The talk is based on
arXiv:0708:2276 with Lionel Mason.
I will discuss a solution generating technique that allows to generate
stationary axisymmetric solutions of five-dimensional gravity, starting
from static ones. This technique can be used to add angular momentum
to static configurations. It can also be used to add KK-monopole charge
to asymptotically flat five-dimensional solutions, thus generating geometries
that interpolate between five-dimensional and four-dimensional solutions.