Week 22.03.2009 – 28.03.2009

In this talk, I will present several results concerning a class of supersymmetric Wilson loop operators in N=4 SYM. These operators can be defined for any loop on a three-sphere and are in general 1/16-BPS. On the string theory side of the AdS/CFT duality, these supersymmetric Wilson loops are described by string worldsheets which are pseudo-holomorphic with respect to a novel almost complex structure defined on a AdS4xS2 subspace of AdS5xS5. A notable subclass of the general 1/16-BPS operators, which will be the main focus of this talk, is obtained by restricting the loop to lie on a S2 in space-time. In this case supersymmetry is doubled, and we propose a conjecture that the expectation value of these operators can be computed exactly in terms of the analogous observables in bosonic 2d Yang-Mills on S2, or equivalently by a gaussian matrix model. Several evidences for this conjecture, both on the gauge theory and on the string theory side, will be presented.

When a salt-stratified fluid is cooled from the side, a two-dimensional convection pattern of cells is formed along the vertical side-wall and develops into horizontal intrusions which grow away from the wall. Such conditions exist in the oceans along melting icebergs, and the growth of these intrusions prevents melt-water from rising to the surface. As the intrusions grow, a series of layers is created in the salt water, with stepped temperature and salinity profiles. In this talk, I will describe an experimental and theoretical study carried out while at the ITG in Cambridge on the formation and growth of these double-diffusive intrusions. Observations were made of growth rates of the intrusions, of internal velocities, and of temperature and salinity distributions. The rate of growth of the intrusions was found, surprisingly, to depend on the length of the experimental tank, with the end-wall playing a role in their evolution right from the beginning of the experiment (Malki-Epshtein, Phillips and Huppert, JFM 2004). Internal waves are visualised using particle tracing methods and are shown to propagate throughout the experimental tank, maintaining hydrostatic equilibrium and having a strong role in setting up the layers. Future application of the results of this study to the large scale could have significant implications for the modelling of oceanic double-diffusive processes, which are believed to drive large vertical and lateral fluxes of heat and salt.

We introduce the Wilson loop/amplitude duality, which states that certain gluon amplitudes in N=4 SYM are equivalent to light-like polygonal Wilson loops. We will illustrate the duality's power by computing the one loop Wilson loop analytically (matching with the known amplitudes) and then the two loop Wilson loop numerically for any number of edges. If the duality continues to hold we can thus compute two loop MHV amplitudes for any number of incoming particles. In the second part of the talk we discuss the recently conjectured new symmetry dual superconformal symmetry of the complete S-matrix of N=4 SYM. We prove its presence at tree-level and find new constraints it puts on the one loop amplitude.