Particle Physics

For more than 70 years, astronomers have had the uneasy suspicion that there was more to the universe than met the eye - much, much more. In the past five years, this suspicion has become a certainty. We now know for sure that normal matter and normal radiation account for only 4% of the density of the universe. One of the two biggest components, dark matter, may be finally be identified by new experiments coming on line next year. I\'ll summarise the long quest to identify dark matter and our prospects for finally achieving this goal in the next two years.

This talk discusses Einstein\'s special and general theories of relativity in a simple manner. Some simple mathematical arguments are included. This leads to a brief description of Loop Quantum Gravity - one of the most popular way of trying to describe gravity using the ideas of quantum mechanics. In addition, the Standard model of particle physics, which describes all known particles and their (non-gravitational) interactions is explained. We conclude with a description of some recent research which may bring the Standard Model and Loop Quantum Gravity together into a single theory.

Modern motivations for extra spacetime dimensions will be presented, in particular the surprising AdS/CFT connection to particle compositeness. It will be shown how highly curved, "warped", extra-dimensional geometries can naturally address several puzzles of fundamental physics, including the weakness of gravity, particle mass hierarchies, dark matter, and supersymmetry breaking. The possibility of direct discovery of warped dimensions at particle colliders such as the CERN Large Hadron Collider will be discussed. Some current questions in warped cosmology will also be introduced.

Some of the speculations on new physics, beyond what is in the standard model are reviewed. Particular attention is paid to ideas that try to address the hierarchy puzzle, i.e., why is the weak scale so much smaller than the Planck scale. These new theories will be tested at the large hadron collider in the near future.

With a cosmic flight simulator, we'll take a scenic journey through space and time. After exploring our local Galactic neighborhood, we'll travel back 13.7 billion years to explore the Big Bang itself and how state-of-the-art measurements are transforming our understanding of our cosmic origin and ultimate fate. We then turn to the question of whether this can all be described purely mathematically, and discuss implications ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like parallel universes, simulations and and Goedel incompleteness.

We consider N=2 supersymmetric quantum electrodynamics (SQED) with 2 flavors, the Fayet--Iliopoulos parameter, and a mass term $beta$ which breaks the extended supersymmetry down to N=1. The bulk theory has two vacua; at $beta=0$ the BPS-saturated domain wall interpolating between them has a moduli space parameterized by a U(1) phase $sigma$ which can be promoted to a scalar field in the effective low-energy theory on the wall world-volume. At small nonvanishing $beta$ this field gets a sine-Gordon potential. As a result, only two discrete degenerate BPS domain walls survive. We find an explicit solitonic solution for domain lines -- string-like objects living on the surface of the domain wall which separate wall I from wall II. The domain line is seen as a BPS kink in the world-volume effective theory. The domain line carries the magnetic flux which is exactly 1/2 of the flux carried by the flux tube living in the bulk on each side of the wall. Thus, the domain lines on the wall confine charges living on the wall, resembling Polyakov's three-dimensional confinement.

I begin with a brief description of the black strings in backgrounds with compact circle, the Gregory-Laflamme instability and the resulting phase transition, and the critical dimensions.Then I describe a Landau-Ginzburg thermodynamic perspective on the instability and on the order of the phase transition. Next, the approach is generalized from a circle compactification to an arbitrary torus compactification. It is shown that the transition order depends only on the number of extended dimensions. I end up with outlining several open questions and puzzles related to the outcome of the Gregory-Laflamme instability.

We discuss the properties of matter in the low temperature regime at density that may exist in the core of compact stars. Assuming that in these conditions quarks are deconfined the attractive color interaction determines the formation of Cooper pairs of quarks and the resulting quark matter has properties analogous to standard superconductors. We show that under reasonable conditions a state were Cooper pairs have non-zero total momentum is energetically favored and the resulting non-homogeneous condensate is characterized by a crystal symmetry. Studying the elastic properties of such a state we find that it behaves like a solid crystal with a very large shear modulus. Our results raise the possibility that (some) pulsar glitches may originate within the Crystalline Color Superconductor core of Neutron stars.