Update on the Pyramid Scheme

We summarize recent work in which we attempt to make a consistent model of LHC physics, from the Pyramid Scheme. The models share much with the NMSSM, in particular, enhanced tree level contributions to the Higgs mass and a preference for small tan {\beta}. There are 3 different singlet fields, and a new strongly coupled gauge theory, so the constraints of perturbative unification are quite different. We outline our general approach to the model, which contains a Kahler potential for three of the low energy fields, which is hard to calculate. Detailed calculations, based on approximations to the Kahler potential, will be presented in a future publication.Comment: LaTeX 2e/ 9 page

A Pyramid Scheme for Particle Physics

We introduce a new model, the Pyramid Scheme, of direct mediation of SUSY breaking, which is compatible with the idea of Cosmological SUSY Breaking (CSB). It uses the trinification scheme of grand unification and avoids problems with Landau poles in standard model gauge couplings. It also avoids problems, which have recently come to light, associated with rapid stellar cooling due to emission of the pseudo Nambu-Goldstone Boson (PNGB) of spontaneously broken hidden sector baryon number. With a certain pattern of R-symmetry breaking masses, a pattern more or less required by CSB, the Pyramid Scheme leads to a dark matter candidate that decays predominantly into leptons, with cross sections compatible with a variety of recent observations. The dark matter particle is not a thermal WIMP but a particle with new strong interactions, produced in the late decay of some other scalar, perhaps the superpartner of the QCD axion, with a reheat temperature in the TeV range. This is compatible with a variety of scenarios for baryogenesis, including some novel ones which exploit specific features of the Pyramid Scheme.Comment: JHEP Latex, 32 pages, 1 figur

Making Sense Of The New Cosmology

Over the past three years we have determined the basic features of the Universe -- spatially flat; accelerating; comprised of 1/3 a new form of matter, 2/3 a new form of energy, with some ordinary matter and a dash of massive neutrinos; and apparently born from a burst of rapid expansion during which quantum noise was stretched to astrophysical size seeding cosmic structure. The New Cosmology greatly extends the highly successful hot big-bang model. Now we have to make sense of all this: What is the dark matter particle? What is the nature of the dark energy? Why this mixture? How did the matter -- antimatter asymmetry arise? What is the underlying cause of inflation (if it indeed occurred)?Comment: 17 pages Latex (sprocl.sty). To appear in the Proceedings of 2001: A Spacetime Odyssey (U. Michigan, May 2001, World Scientific

Is There A String Theory Landscape

We examine recent claims of a large set of flux compactification solutions of string theory. We conclude that the arguments for AdS solutions are plausible. The analysis of meta-stable dS solutions inevitably leads to situations where long distance effective field theory breaks down. We then examine whether these solutions are likely to lead to a description of the real world. We conclude that one must invoke a strong version of the anthropic principle. We explain why it is likely that this leads to a prediction of low energy supersymmetry breaking, but that many features of anthropically selected flux compactifications are likely to disagree with experiment.Comment: 39 pages, Latex, ``Terminology surrounding the anthropic principle revised to conform with accepted usage. More history of the anthropic principle included. Various references added.

Model validation for a noninvasive arterial stenosis detection problem

Copyright @ 2013 American Institute of Mathematical SciencesA current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use both one-dimensional pressure and shear wave experimental data from novel acoustic phantoms to validate corresponding viscoelastic mathematical models, which were developed in a concept paper [8] and refined herein. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.The National Institute of Allergy and Infectious Diseases, the Air Force Office of Scientific Research, the Deopartment of Education and the Engineering and Physical Sciences Research Council (EPSRC)

Supersymmetry, the Cosmological Constant and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterize different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models. This essay was submitted to the Gravity Research Foundation Competition and is based on a longer article, which will be submitted in the near future

Vertex Operators in 2K Dimensions

A formula is proposed which expresses free fermion fields in 2K dimensions in terms of the Cartan currents of the free fermion current algebra. This leads, in an obvious manner, to a vertex operator construction of nonabelian free fermion current algebras in arbitrary even dimension. It is conjectured that these ideas may generalize to a wide class of conformal field theories.Comment: Minor change in notation. Change in references

Dynamical Systems On Three Manifolds Part II: 3-Manifolds,Heegaard Splittings and Three-Dimensional Systems

The global behaviour of nonlinear systems is extremely important in control and systems theory since the usual local theories will only give information about a system in some neighbourhood of an operating point. Away from that point, the system may have totally different behaviour and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on 2- and 3- manifolds and show that it is possible to obtain systems with 'arbitrarily strange' behaviour, i.e., arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.Comment: 15 pages with 9 pictures. Accepted by Int. J. of Bifurcation and Chao

Nonsingular Lagrangians for Two Dimensional Black Holes

We introduce a large class of modifications of the standard lagrangian for two dimensional dilaton gravity, whose general solutions are nonsingular black holes. A subclass of these lagrangians have extremal solutions which are nonsingular analogues of the extremal Reissner-Nordstrom spacetime. It is possible that quantum deformations of these extremal solutions are the endpoint of Hawking evaporation when the models are coupled to matter, and that the resulting evolution may be studied entirely within the framework of the semiclassical approximation. Numerical work to verify this conjecture is in progress. We point out however that the solutions with non-negative mass always contain Cauchy horizons, and may be sensitive to small perturbations.Comment: 27 pages, three figures, RU-92-61. (Replaced version contains some corrections to incorrect equations. The zero temperature extremal geometry (the conjectured end-point of the Hawking evaporation) is not as stated in the previous version, but rather is a nonsingular analogue of the zero temperature $M^2 = Q^2$ Reissner-Nordstrom space-time.

4d Conformal Field Theories and Strings on Orbifolds

We propose correspondences between 4d quantum field theories with N=2,1,0 (super)conformal invariance and Type IIB string theory on various orbifolds. We argue using the spacetime string theory, and check using the beta functions (exactly for N=2,1 and so far at 1-loop for the gauge couplings in the N=0 case), that these theories have conformal fixed lines. The latter case potentially gives well-defined non-supersymmetric vacua of string theory, with a mechanism for making the curvature and cosmological constant small at nontrivial string coupling. We suggest a correspondence between nonsupersymmetric conformal fixed lines and nonsupersymmetric string vacua with vanishing vacuum energy.Comment: 11 pages, harvmac big. Reference adde