Future Summary

We are emerging from a period of consolidation in particle physics. Its great, historic achievement was to establish the Theory of Matter. This Theory will serve as our description of ordinary matter under ordinary conditions -- allowing for an extremely liberal definition of "ordinary -- for the foreseeable future. Yet there are many indications, ranging from the numerical to the semi-mystical, that a new fertile period lies before us. We will discover compelling evidence for the unification of fundamental forces and for new quantum dimensions (low-energy supersymmetry). We will identify new forms of matter, which dominate the mass density of the Universe. We will achieve much better fundamental understanding of the behavior of matter in extreme astrophysical and cosmological environments. Lying beyond these expectations, we can identify deep questions that seem to call for ideas outside our present grasp. And there's still plenty of room for surprises.Comment: 25 pages, 13 EPS figures, LaTeX with BoxedEPS macros. Closing talk delivered at the LEPfest, CERN, October 11, 2000. Email correspondence to [email protected]

Advantages and Distinguishing Features of Focus Point Supersymmetry

Diverse experimental constraints now motivate models of supersymmetry breaking in which some superpartners have masses well above the weak scale. Three alternatives are focus point supersymmetry and inverted hierarchy models, which embody a naturalness constraint, and the more recent framework of split supersymmetry, which relaxes that constraint. Many aspects of their phenomenology are very similar. They can be distinguished, however, through detailed study of superoblique parameters, the Higgs potential and other observables.Comment: 9 pages, published versio

Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N)

We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined on a two-dimensional lattice, the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q = e^{i\pi\nu}$. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebra.Comment: 13p LaTeX Document (should be run twice

Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana bound states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark state subspace.Comment: 4 pages; Add detailed discussion of feasibility of the scheme;add ref

Asymptotic Freedom: From Paradox to Paradigm

Asymptotic freedom was developed as a response to two paradoxes: the weirdness of quarks, and in particular their failure to radiate copiously when struck; and the coexistence of special relativity and quantum theory, despite the apparent singularity of quantum field theory. It resolved these paradoxes, and catalyzed the development of several modern paradigms: the hard reality of quarks and gluons, the origin of mass from energy, the simplicity of the early universe, and the power of symmetry as a guide to physical law.Comment: 26 pages, 10 figures. Lecture on receipt of the 2004 Nobel Prize. v2: typo (in Ohm's law) correcte

Minimal Potentials with Very Many Minima

We demonstrate, by construction, that simple renormalizable matrix potentials with S_N, as opposed to O(N), symmetry can exhibit an exponentially large number of inequivalent deep local minima.Comment: LaTeX, 9 pages, 2 figures. Additional applications and references adde

Systematic Study Of Leptonic Mixing In A Class Of SU_H(2) Models

We perform a systematic analysis of the PMNS matrices which arise when one assigns the three generations of leptons to the $2\oplus 1$ representation of a horizontal $SU_H(2)$ symmetry. This idea has been previously explored by Kuchimanchi and Mohapatra. However, we assume $(i)$ the neutrino mass matrix results from leptonic couplings to $SU_L(2)$ triplet scalar fields and $(ii)$ hierarchies exist amongst lepton mass matrix elements which result from couplings to scalar fields with different $SU_H(2)$ charges. Of the sixteen candidate PMNS matrices which result it is found that only one is both predictive and possesses a leading order structure compatible with experimental data. The relevant neutrino mass matrix displays the symmetry $L_e-L_\mu-L_\tau$ to leading order and we explore the perturbations required to produce a realistic lepton spectrum. The effective mass in neutrinoless double beta decay is required to lie in the range $/(10^{-2}\mathrm{eV})\in[0.7,2.5]$, which is just below current experimental bounds. $U_{e3}$ is non-zero but not uniquely determined.Comment: To appear in Phys. Rev.

Quantum Numbers of Textured Hall Effect Quasiparticles

We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue that the spin of the corresponding quasiparticle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.Comment: 13 pages, no figures, Phyzz

Theory for the single-point velocity statistics of fully developed turbulence

We investigate the single-point velocity probability density function (PDF) in three-dimensional fully developed homogeneous isotropic turbulence within the framework of PDF equations focussing on deviations from Gaussianity. A joint analytical and numerical analysis shows that these deviations may be quantified studying correlations of dynamical quantities like pressure gradient, external forcing and energy dissipation with the velocity. A stationary solution for the PDF equation in terms of these quantities is presented, and the theory is validated with the help of direct numerical simulations indicating sub-Gaussian tails of the PDF.Comment: 6 pages, 4 figures, corrected typo in eq. (4