Thomas W. Kephart

Solutions to the strong CP problem in a world with gravity

We examine various solutions of the strong-CP problem to determine their sensitivity to possible violations of global symmetries by Plauck scale physics. While some solutions remain viable even in the face of such effects. Violations of the Peccei-Quinn (PQ) symmetry by non-renormalizable operators of dimension less than 10 will generally shift the value of {bar {theta}} to values inconsistent with the experimental bound {bar {theta}} {approx_lt} 10{sup {minus}}9. We show that it is possible to construct axion models where gauge symmetries protect PQ symmetry to the requisite level.

SIMPLE NON-ABELIAN FINITE FLAVOR GROUPS AND FERMION MASSES

The use of non-Abelian discrete groups G as family symmetries is discussed in detail. Out of all such groups up to order g=31, the most appealing candidates are two subgroups of SU(2): the dicyclic (double dihedral) group G=Q6=(d)D3(g=12) and the double tetrahedral group . Both can allow a hierarchy t>b, τ>c>s, μ>u, d, e. The top quark is uniquely allowed to have a G symmetric mass. Sequential breaking of G and radiative corrections give the smaller masses. Anomaly freedom for gauging G⊂SU(2) is a strong constraint in assignment of fermions to representations of G.

LieART—A Mathematica application for Lie algebras and representation theory

Abstract We present the Mathematica application “LieART” ( Lie A lgebras and R epresentation T heory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART’s user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included as online supplementary material (see Appendix A ). Program summary Program title: LieART Catalogue identifier: AEVL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License No. of lines in distributed program, including test data, etc.: 183178 No. of bytes in distributed program, including test data, etc.: 411658 Distribution format: tar.gz Programming language: Mathematica. Computer: x86, x86_64, PowerPC. Operating system: cross-platform. RAM: ≥ 1 GB recommended. Memory usage depends strongly on the Lie algebra’s rank and type, as well as the dimensionality of the representations in the computation. Classification: 4.2, 11.1. External routines: Wolfram Mathematica 8-10 Nature of problem: The use of Lie algebras and their representations is widespread in physics, especially in particle physics. The description of nature in terms of gauge theories requires the assignment of fields to representations of compact Lie groups and their Lie algebras. Mass and interaction terms in the Lagrangian give rise to the need for computing tensor products of representations of Lie algebras. The mechanism of spontaneous symmetry breaking leads to the application of subalgebra decomposition. This computer code was designed for the purpose of Grand Unified Theory (GUT) Model building, where compact Lie groups beyond the U(1), SU(2) and SU(3) of the Standard Model of particle physics are needed. Tensor product decomposition and subalgebra decomposition have been implemented for all classical Lie groups SU ( N ) , SO ( N ) and Sp ( 2 N ) and the exceptionals E6, E7, E8, F4 and G2. Solution method: LieART generates the weight system of an irreducible representation (irrep) of a Lie algebra by exploiting the Weyl reflection groups, which is inherent in all simple Lie algebras. Tensor products are computed by the application of Klimyk’s formula, except for SU ( N ) ’s, where the Young-tableaux algorithm is used. Subalgebra decomposition of SU ( N ) ’s are performed by projection matrices, which are generated from an algorithm to determine maximal subalgebras as originally developed by Dynkin [1, 2]. Restrictions: Internally irreps are represented by their unique Dynkin label. LieART’s default behavior in TraditionalForm is to print the dimensional name, which is the labeling preferred by physicists. Most Lie algebras can have more than one irrep of the same dimension and different irreps with the same dimension are usually distinguished by one or more primes (e.g. 175 and 175 ′ of A 4 ). To determine the need for one or more primes of an irrep a brute-force loop over other irreps must be performed to search for irreps with the same dimensionality. Since Lie algebras have an infinite number of irreps, this loop must be cut off, which is done by limiting the maximum Dynkin digit in the loop. In rare cases for irreps of high dimensionality in high-rank algebras, if the cutoff used is too low, then the assignment of primes will be incorrect, but the problem can be avoided by raising the cutoff. However, in either case, this can only affect the display of the irrep because all computations involving this irrep are correct, since the internal unique representation of Dynkin labels is used. Running time: From less than a second to hours depending on the Lie algebra’s rank and type and/or the dimensionality of the representations in the computation. References: [1] E. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Trans. Am. Math. Soc. 6 (1957) 111. [2] E. Dynkin, Maximal subgroups of the classical groups, Trans. Am. Math. Soc. 6 (1957) 245.

What is the entropy of the universe

Standard calculations suggest that the entropy of our universe is dominated by black holes, whose entropy is of order their area in Planck units, although they comprise only a tiny fraction of its total energy. Statistical entropy is the logarithm of the number of microstates consistent with the observed macroscopic properties of a system, hence a measure of uncertainty about its precise state. Therefore, assuming unitarity in black hole evaporation, the standard results suggest that the largest uncertainty in the future quantum state of the universe is due to the Hawking radiation from evaporating black holes. However, the entropy of the matter precursors to astrophysical black holes is enormously less than that given by area entropy. If unitarity relates the future radiation states to the black hole precursor states, then the standard results are highly misleading, at least for an observer that can differentiate the individual states of the Hawking radiation.

Magnetic monopoles as the highest energy cosmic ray primaries

Abstract We suggest that the highest energy ≳ 10 20 eV cosmic ray primaries may be relativistic magnetic monopoles. Motivations for this hypothesis are that conventional primaries are problematic, while monopoles are naturally accelerated to E ∼ 10 20 eV by galactic magnetic fields. By matching the cosmic monopole production mechanism to the observed highest energy cosmic ray flux we estimate the monopole mass to be ≲ 10 10 GeV.

Classification of Conformality Models Based on Nonabelian Orbifolds

A systematic analysis is presented of compactifications of the IIB superstring on AdS5×S 5 / where is a non-abelian discrete group. Every possible wi th order g ≤ 31 is considered. There exist 45 such groups but a majority cannot yield chiral fermions due to a certain theorem that is proved. The lowest order to embrace the nonSUSY standard SU(3) × SU(2) × U(1) model with three chiral families is = D4 × Z3, with g = 24; this is the only successful model found in the search. The consequent uniqueness of the successful model arises primarily from the scalar sector, prescribed by the construction, being

A model of glueballs

We model the observed glueball mass spectrum in terms of energies for tightly knotted and linked QCD flux tubes. The data is fit well with one parameter. We predict additional glueball masses.

From spacetime foam to holographic foam cosmology

Abstract Due to quantum fluctuations, spacetime is foamy on small scales. For maximum spatial resolution of the geometry of spacetime, the holographic model of spacetime foam stipulates that the uncertainty or fluctuation of distance l is given, on the average, by ( l l P 2 ) 1 / 3 where l P is the Planck length. Applied to cosmology, it predicts that the cosmic energy is of critical density and the cosmic entropy is the maximum allowed by the holographic principle. In addition, it requires the existence of unconventional (dark) energy/matter and accelerating cosmic expansion in the present era. We will argue that a holographic foam cosmology of this type has the potential to become a full fledged competitor (with distinct testable consequences) for scalar driven inflation.

Analytical Debye-Huckel model for electrostatic potentials around dissolved DNA

We present an analytical, Green-function-based model for the electric potential of DNA in solution, treating the surrounding solvent with the Debye-Huckel approximation. The partial charge of each atom is accounted for by modeling DNA as linear distributions of atoms on concentric cylindrical surfaces. The condensed ions of the solvent are treated with the Debye-Huckel approximation. The resultant leading term of the potential is that of a continuous shielded line charge, and the higher order terms account for the helical structure. Within several angstroms of the surface there is sufficient information in the electric potential to distinguish features and symmetries of DNA. Plots of the potential and equipotential surfaces, dominated by the phosphate charges, reflect the structural differences between the A, B, and Z conformations and, to a smaller extent, the difference between base sequences. As the distances from the helices increase, the magnitudes of the potentials decrease. However, the bases and sugars account for a larger fraction of the double helix potential with increasing distance. We have found that when the solvent is treated with the Debye-Huckel approximation, the potential decays more rapidly in every direction from the surface than it did in the concentric dielectric cylinder approximation.

The Eccentric universe

For a universe containing a cosmological constant together with uniform arrangements of magnetic fields, strings, or domain walls, exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal expansion. The magnetic field case is the easiest to motivate and has the highest possibility of finding application in observational cosmology.