Scientific Series

The Rozansky-Witten model is a topological sigma-model in three dimensions whose target is a hyper-Kahler manifold. Upon compactification to 2d it reduces to the B-model with the same target. Boundary conditions for the Rozansky-Witten model can be regarded as a 3d generalization of B-branes. While branes form a category, boundary conditions in a 3d TFT form a 2-category. I will describe the structure of this 2-category for the Rozansky-Witten model and its connection with a categorification of deformation quantization. I will also discuss defects of codimension 1 (domain walls) and defects of codimension 2 (line operators) in the Rozansky-Witten model.

In topological quantum computation the geometric details of a particle trajectory become irrelevant; only the topology matters. This is one reason for the inherent fault tolerance of topological quantum computation. I will speak about a model in which this idea is taken one step further. Even the topology is irrelevant. The computation is determined solely by the permutation of the particles. Unlike topological quantum computation, which requires anyons confined to two dimensions, permutational quantum computations can in principle be performed by permuting a set of ordinary spin-1/2 particles with definite total angular momentum in three dimensions. The resulting model of computation appears to be intermediate in power between classical computation (P) and standard quantum computation (BQP). The model may be equivalently defined in terms of spin networks, which are an important concept in loop quantum gravity.

Quantum mechanics is a non-classical probability theory, but hardly the most general one imaginable: any compact convex set can serve as the state space for an abstract probabilistic model (classical models corresponding to simplices). From this altitude, one sees that many phenomena commonly regarded as ``characteristically quantum' are in fact generically ``non-classical'. In this talk, I'll show that almost any non-classical probabilistic theory shares with quantum mechanics a notion of entanglement and, with this, a version of the so-called measurement problem. I'll then discuss what's required for an abstract probabilistic theory to admit a somewhat simplified version of Everett's response to this problem -- an exercise that turns out to be instructive in several ways.

We consider a probe codimension-2 brane inflation scenario in a warped six-dimensional flux compactification. First, we stabilise the modulus of the model by means of a cap regularisation of the codimension-2 singularities of the background solution. Then, we discuss the cosmological evolution of the world-volume of a probe codimension-2 brane when it moves along the radial direction of the internal space. In order to have slow-roll inflation, one needs the warping of the internal space to be weak, in contrast to the recent string inflation constructions with strong warping. We discuss the parameter range that the inflation is in agreement with the observationally inferred parameters and which furthermore is consistent with the probe brane approximation. We show that this scenario is falsifiable if substantial tensor modes are detected.

I will compute the probability distribution for bubble collisions in an inflating false vacuum which decays by bubble nucleation. The number of collisions in our backward lightcone can be large in realistic models without tuning. In addition, we calculate the angular position and size distribution of the collisions on the cosmic microwave background sky.

The ATLAS experiment at the Large Hadron Collider (LHC) at CERN is completing final preparations for first high energy collisions in 2009. This talk will cover: the physics motivation of the LHC, highlights of the ATLAS experiment, commissioning, and prospects for new physics discoveries ahead.

I will report results from simulations of galaxy-scale dark halos of unprecedented numerical resolution. Convergence tests demonstrate detailed convergence for (sub)structures for over six decades in mass, enabling detailed forecasts of the expected dark matter signal both in Earth-bound direct-detection experiments as well as in indirect detection experiments which attempt to image dark matter annihilation radiation in gamma rays.

Varied experimental results have recently sparked theoretical interest in the dark matter sector. I will review some of these results and the basic ideas in particle physics that might explain them, as well as some requirements for those models to work. Then I'll discuss a new model dark matter sector that can better explain many of the experimental results. I'll also mention the interesting cosmological history required in this type of model. Finally, if there's time, I'll discuss ongoing efforts at McGill to develop basic physics shared by many of the new dark matter models.

Brane Tilings are known to describe the largest known class of SCFT's in 3+1 dimensions. There is a well established formalism to find AdS_5 x SE_5 duals to these SCFT's and to compare results on both sides. This talk extends this formalism to 2+1 dimensional SCFT's, living on the world volume of M2 branes, which are dual to AdS_4 x SE_7 backgrounds of M theory. The SCFT's are quiver gauge theories with 4 supercharges (N=2 in 2+1 dimensions) and Chern Simons (CS) couplings. They admit a moduli space of vacuum configurations which is a CY4 cone over SE_7. The talk will go over the formalism and look at several examples in detail. The computation of scaling dimensions will be mentioned and relations to regular toric Fano 3-folds if time permits.

An electroweak model in which the masses of the W and Z bosons and the fermions are generated by quantum loop graphs through a symmetry breaking of the vacuum is investigated. The model is based on a regularized quantum field theory in which the quantum loop graphs are finite to all orders of perturbation theory and the massless theory is gauge invariant, Poincaré invariant, and unitary to all orders. The breaking of the electroweak symmetry SUL(2) × UY (1) is achieved without a Higgs particle. A fundamental energy scale ΛW (not to be confused with a naive cutoff) enters the theory through the regularization of the Feynman loop diagrams. The finite regularized theory with ΛW allows for a fitting of low energy electroweak data. ΛW ~ 542 GeV is determined at the Z pole by fitting it to the Z mass mZ, and anchoring the value of sin²θw to its experimental value at the Z pole yields a prediction for the W mass mW that is accurate to about 0.5% without radiative corrections. The scattering amplitudes for WLWL → WLWL and e+e− → W+L W−L processes do not violate unitarity at high energies due to the suppression of the amplitudes by the running of the coupling constants at vertices. There is no Higgs hierarchy fine-tuning problem in the model. The unitary tree level amplitudes for WLWL → WLWL scattering and e+e− → W+L W−L annihilation, predicted by the finite electroweak model are compared with the amplitudes obtained from the standard model with Higgs exchange. These predicted amplitudes can be used to distinguish at the LHC between the standard electroweak model and the Higgsless model.

The standard cosmological framework explains an impressive range of large-scale astrophysical phenomena, but an agreement between its predictions and the properties of the dark matter halos of nearby galaxies has not been established. In this talk, I will highlight some key observables that constrain galaxy structure and some key differences between cosmological predictions and halo properties inferred from these measurements. I will also discuss proposed 'observational' solutions to some of these discrepancies, such as the role of coherent non-circular motions in spiral galaxies and the measured abundance of gas-rich, starless halos in the nearby Universe.