Towards a quantum theory of de Sitter space

We describe progress towards constructing a quantum theory of de Sitter space in four dimensions. In particular we indicate how both particle states and Schwarzschild de Sitter black holes can arise as excitations in a theory of a finite number of fermionic oscillators. The results about particle states depend on a conjecture about algebras of Grassmann variables, which we state, but do not prove.Comment: JHEP3 LaTex - 19 page

Embedding the Pentagon

The Pentagon Model is an explicit supersymmetric extension of the Standard Model, which involves a new strongly-interacting SU(5) gauge theory at TeV-scale energies. We show that the Pentagon can be embedded into an SU(5) x SU(5) x SU(5) gauge group at the GUT scale. The doublet-triplet splitting problem, and proton decay compatible with experimental bounds, can be successfully addressed in this context. The simplest approach fails to provide masses for the lighter two generations of quarks and leptons; however, this problem can be solved by the addition of a pair of antisymmetric tensor fields and an axion.Comment: 39 page

Decoupling a Fermion Whose Mass Comes from a Yukawa Coupling: Nonperturbative Considerations

Perturbative analyses seem to suggest that fermions whose mass comes solely from a Yukawa coupling to a scalar field can be made arbitrarily heavy, while the scalar remains light. The effects of the fermion can be summarized by a local effective Lagrangian for the light degrees of freedom. Using weak coupling and large N techniques, we present a variety of models in which this conclusion is shown to be false when nonperturbative variations of the scalar field are considered. The heavy fermions contribute nonlocal terms to the effective action for light degrees of freedom. This resolves paradoxes about anomalous and nonanomalous symmetry violation in these models. Application of these results to lattice gauge theory imply that attempts to decouple lattice fermion doubles by the method of Swift and Smit cannot succeed, a result already suggested by lattice calculations.Comment: 31 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

Toward a Background Independent Quantum Theory of Gravity

Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a novel, background independent non-perturbative formulation of quantum gravity. We invoke a quantum version of the equivalence principle, which requires both the statistical and symplectic geometries of canonical quantum theory to be fully dynamical quantities. Our approach sheds new light on such basic issues of quantum gravity as the nature of observables, the problem of time, and the physics of the vacuum. In particular, the observed numerical smallness of the cosmological constant can be rationalized in this approach.Comment: Awarded Honorable Mention, 2004 Gravity Research Foundation Essay Competition; 8 pages, LaTe

Algebras, Derivations and Integrals

In the context of the integration over algebras introduced in a previous paper, we obtain several results for a particular class of associative algebras with identity. The algebras of this class are called self-conjugated, and they include, for instance, the paragrassmann algebras of order $p$, the quaternionic algebra and the toroidal algebras. We study the relation between derivations and integration, proving a generalization of the standard result for the Riemann integral about the translational invariance of the measure and the vanishing of the integral of a total derivative (for convenient boundary conditions). We consider also the possibility, given the integration over an algebra, to define from it the integral over a subalgebra, in a way similar to the usual integration over manifolds. That is projecting out the submanifold in the integration measure. We prove that this is possible for paragrassmann algebras of order $p$, once we consider them as subalgebras of the algebra of the $(p+1)\times(p+1)$ matrices. We find also that the integration over the subalgebra coincides with the integral defined in the direct way. As a by-product we can define the integration over a one-dimensional Grassmann algebra as a trace over $2\times 2$ matrices.Comment: 23 pages, few typos corrected. Final version to be published in International Journal of Modern Physic

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)

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.

Estimation of coefficients and boundary parameters in hyperbolic systems

Semi-discrete Galerkin approximation schemes are considered in connection with inverse problems for the estimation of spatially varying coefficients and boundary condition parameters in second order hyperbolic systems typical of those arising in 1-D surface seismic problems. Spline based algorithms are proposed for which theoretical convergence results along with a representative sample of numerical findings are given

Supersymmetric extension of Moyal algebra and its application to the matrix model

We construct operator representation of Moyal algebra in the presence of fermionic fields. The result is used to describe the matrix model in Moyal formalism, that treat gauge degrees of freedom and outer degrees of freedom equally.Comment: to appear in Mod.Phys.Let