Winding Solutions for the two Particle System in 2+1 Gravity

Using a PASCAL program to follow the evolution of two gravitating particles in 2+1 dimensions we find solutions in which the particles wind around one another indefinitely. As their center of mass moves `tachyonic' they form a Gott-pair. To avoid unphysical boundary conditions we consider a large but closed universe. After the particles have evolved for some time their momenta have grown very large. In this limit we quantize the model and find that both the relevant configuration variable and its conjugate momentum become discrete.Comment: 15 pages Latex, 4 eps figure

TransPlanckian Particles and the Quantization of Time

Trans-Planckian particles are elementary particles accelerated such that their energies surpass the Planck value. There are several reasons to believe that trans-Planckian particles do not represent independent degrees of freedom in Hilbert space, but they are controlled by the cis-Planckian particles. A way to learn more about the mechanisms at work here, is to study black hole horizons, starting from the scattering matrix Ansatz. By compactifying one of the three physical spacial dimensions, the scattering matrix Ansatz can be exploited more efficiently than before. The algebra of operators on a black hole horizon allows for a few distinct representations. It is found that this horizon can be seen as being built up from string bits with unit lengths, each of which being described by a representation of the SO(2,1) Lorentz group. We then demonstrate how the holographic principle works for this case, by constructing the operators corresponding to a field in space-time. The parameter t turns out to be quantized in Planckian units, divided by the period R of the compactified dimension.Comment: 12 pages plain tex, 1 figur

The mathematical basis for deterministic quantum mechanics

If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes. The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.Comment: 17 pages, 3 figures. Minor corrections, comments and explanations adde

Pauli-Lubanski scalar in the Polygon Approach to 2+1-Dimensional Gravity

In this paper we derive an expression for the conserved Pauli-Lubanski scalar in 't Hooft's polygon approach to 2+1-dimensional gravity coupled to point particles. We find that it is represented by an extra spatial shift $\Delta$ in addition to the usual identification rule (being a rotation over the cut). For two particles this invariant is expressed in terms of 't Hooft's phase-space variables and we check its classical limit.Comment: Some errors are corrected and a new introduction and discussion are added. 6 pages Latex, 4 eps-figure

A Chiral SU(N) Gauge Theory Planar Equivalent to Super-Yang-Mills

We consider the dynamics of a strongly coupled SU(N) chiral gauge theory. By using its large-N equivalence with N=1 super-Yang-Mills theory we find the vacuum structure of the former. We also consider its finite-N dynamics.Comment: 10 pages, Latex. 1 eps figur

Understanding Confinement From Deconfinement

We use effective magnetic SU(N) pure gauge theory with cutoff M and fixed gauge coupling g_m to calculate non-perturbative magnetic properties of the deconfined phase of SU(N) Yang-Mills theory. We obtain the response to an external closed loop of electric current by reinterpreting and regulating the calculation of the one loop effective potential in Yang-Mills theory. This effective potential gives rise to a color magnetic charge density, the counterpart in the deconfined phase of color magnetic currents introduced in effective dual superconductor theories of the confined phase via magnetically charged Higgs fields. The resulting spatial Wilson loop has area law behavior. Using values of M and g_m determined in the confined phase, we find SU(3) spatial string tensions compatible with lattice simulations in the temperature interval 1.5T_c < T < 2.5T_c. Use of the effective theory to analyze experiments on heavy ion collisions will provide applications and further tests of these ideas.Comment: 18 pages, 5 figures, v2: fixed archive title (only

Indeterminacy of Holographic Quantum Geometry

An effective theory based on wave optics is used to describe indeterminacy of position in holographic spacetime with a UV cutoff at the Planck scale. Wavefunctions describing spacetime positions are modeled as complex disturbances of quasi-monochromatic radiation. It is shown that the product of standard deviations of two position wavefunctions in the plane of a holographic light sheet is equal to the product of their normal separation and the Planck length. For macroscopically separated positions the transverse uncertainty is much larger than the Planck length, and is predicted to be observable as a "holographic noise" in relative position with a distinctive shear spatial character, and an absolutely normalized frequency spectrum with no parameters once the fundamental wavelength is fixed from the theory of gravitational thermodynamics. The spectrum of holographic noise is estimated for the GEO600 interferometric gravitational-wave detector, and is shown to approximately account for currently unexplained noise between about 300 and 1400Hz. In a holographic world, this result directly and precisely measures the fundamental minimum interval of time.Comment: 4 pages, LaTeX. Considerably shortened from earlier version. Conclusions are unchanged. Submitted to PR

The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity

In this paper we describe the matter-free toroidal spacetime in 't Hooft's polygon approach to 2+1-dimensional gravity (i.e. we consider the case without any particles present). Contrary to earlier results in the literature we find that it is not possible to describe the torus by just one polygon but we need at least two polygons. We also show that the constraint algebra of the polygons closes.Comment: 18 pages Latex, 13 eps-figure

Vanishing chiral couplings in the large-N_C resonance theory

The construction of a resonance theory involving hadrons requires implementing the information from higher scales into the couplings of the effective Lagrangian. We consider the large-Nc chiral resonance theory incorporating scalars and pseudoscalars, and we find that, by imposing LO short-distance constraints on form factors of QCD currents constructed within this theory, the chiral low-energy constants satisfy resonance saturation at NLO in the 1/Nc expansion.Comment: 5 pages, 2 figures. Version published in Physical Review D. Some equations to facilitate the discussion have been adde

Higgsino dark matter in partly supersymmetric models

Models where supersymmetry (SUSY) is manifest only in a sector of the low-energy spectrum have been recently proposed as an alternative to the MSSM. In these models the electroweak scale is explained by a fine-tuning between different Higgs mass contributions (split-SUSY models), or by the localization of the Higgs sector in a point of an extra dimension where all the mass parameters are suppressed by the metric (partly-SUSY models). Therefore, the presence of a good dark matter candidate becomes the main motivation for (partial) low-energy SUSY. We study this issue in minimal frameworks where the higgsinos are the only light supersymmetric particles. Whereas in split-SUSY models the higgsino should have a mass around 1 TeV, we show that in partly-SUSY models the lightest higgsino could also be found below MW.Comment: 12 pages, 3 figures, version to appear in Phys. Rev.