Week 12.10.2009 – 18.10.2009

The 11 year solar magnetic cycle is driven by a hydromagnetic dynamo. However, the exact nature of this dynamo mechanism is still not fully understood, and there are several scenarios proposed to explain the observed behaviour. Here I will briefly overview observations of the solar magnetic field before moving on to discuss why magnetic buoyancy is a key ingredient in the models proposed to explain the observations of the large-scale magnetic field. I will go on to discuss the recent progress in our understanding of magnetic buoyancy with emphasis on double-diffusive magnetic buoyancy.

We consider some novel topological effects, with potentially observable consequences, in classical and quantum gravity. In one scenario, we find that the topology of extra dimensions generically breaks global Lorentz symmetry, leading to distinct experimental signatures in the context of brane worlds. In a different scenario, we show that topological terms in the gravitational action, such as those expected in heterotic string theory, can greatly enhance the instability of four-dimensional de Sitter space by favouring the nucleation of primordial black holes.

Linear statistics on ensembles of random matrices occur frequently in many applications. We present a general method to compute probability distributions of linear statistics for large matrix size N. This is applied to the calculation of conductance and shot noise for ballistic scattering in chaotic cavities, in the limit of large number of open channels. The method is based on a mapping to a Coulomb gas problem in Laplace space, displaying phase transitions as the Laplace parameter is varied. As a consequence, the sought distributions generally display a central Gaussian region flanked on both sides by non-Gaussian tails, and weak non-analytical points at the junction of the two regimes.

There is good evidence that a class of conformal gauge theories at strong gauge coupling and for large rank of the gauge group can be described by classical gravity in five dimensions. In this gauge/gravity duality, the theory of classical gravity always admits a consistent truncation to pure gravity so that there is a sector in the dual gauge theories where the dynamics is universal. This universal sector constitutes phenomena like hydrodynamics, but also other phenomena far away from equilibrium such as decoherence and relaxation. We will use field theoretic tools to understand how the time evolution of all states and the expectation values of all observables in the universal sector get determined by the energy-momentum tensor alone. We will find a way to extrapolate our field-theoretic results to strong coupling to propose a condition on the energy-momentum tensor such that the dual solution in gravity has a smooth future horizon, as a test of our approach. We will also do a first study of how irreversibility emerges at long time scales of observation through gravity.

AdS2-CFT1 correspondence leads to a prescription for computing the degeneracy of a single centered extremal black hole in terms of path integral over string fields living on the near horizon geometry of the extremal black hole. This prescription is called quantum entropy function. In four dimension the near horizon isometry group SL(2,R) x SU(2) for BPS black hole gets enhanced to full SU(1,1,2). Using these enhanced supersymmetries and localization techniques, we will argue that the path integral receives contribution only from special class of field configurations which are invariant under a particular subgroup of SU(1,1,2). We will identify saddle points which are invariant under this subgroup.

Gauge-gravity duality is an extremely useful tool for studying strongly-coupled gauge theories, and has many applications to real-world systems, such as the quark-gluon plasma and quantum critical points. Most gauge-gravity dualities involve a gauge theory with fields only in the adjoint representation of the gauge group. In many strongly-coupled systems, however, such as the quark-gluon plamsa, fields in the fundamental representation of the gauge group, 'flavor fields', are crucially important. For (3+1)-dimensional gauge theories with gravity duals (AdS5/CFT4), the supergravity description of flavor fields is well-understood: flavor fields appear in supergravity as probe D-branes in AdS5. The story for (2+1)-dimensional gauge theories (AdS4/CFT3) is much less developed. Indeed, for supergravity on AdS4 x S7, the dual (2+1)-dimensional field theory (without flavor) was only recently discovered. In this talk I will describe how to add flavor to this theory. In particular, I will present a general recipe to determine the field theory, and in particular the couplings of the flavor fields, given a probe D-brane in AdS4.

A characteristic feature of string theory is the asymptotic nature of the free energy genus expansion indicating the presence of non-perturbative effects due to branes. In certain toy models, such as minimal models or topological strings, the theory admits a matrix model description. In these cases the non-perturbative effects can be interpreted in terms of eigenvalues tunneling in the dual matrix model and the finite N matrix model can be naturally regarded as the non-perturbative completion of the theory. We address the case of the topological string on the Resolved Conifold. We compute the exact non-perturbative contribution to the free energy via Borel analysis and show how it controls the large order behavior of the theory. We interpreted the non-perturbative effects in the dual Chern-Simons matrix models and in the space-time in terms of toric branes.