67793460
Algorithm for determining U(1) charges in free fermionic heterotic string models
To assist in the search for phenomenologically realistic models in the string landscape, we must develop tools for investigating all gauge charges, including U(1) charges, in string models. We introduce the process for constructing fermionic string models and present an algorithm for determining the U(1) gauge states and U(1) charges in weakly-coupled free fermionic heterotic string (WCFFHS) models given their matter and non-Abelian gauge content. We determine the computational complexity of this algorithm and discuss a particular implementation that can be used in conjunction with a framework developed at Baylor University for building WCFFHS models. We also present preliminary results regarding matter state uniqueness for a run of 1.4 million gauge models and find that U(1) charges affect the number of unique matter states in a significant minority of models constructed. We conclude by considering future avenues of investigation to which this algorithm may be applied.
118426859
SYSTEMATIC INVESTIGATIONS OF THE FREE FERMIONIC HETEROTIC STRING GAUGE GROUP STATISTICS: LAYER 1 RESULTS
Using software under development at Baylor University, we explicitly construct all layer 1 gauge, weakly coupled free fermionic heterotic string models up to order 22 in four large spacetime dimensions. The gauge models consist primarily of gauge content making a systematic construction process efficient. We present an overview of the model building procedure, redundancies in the process, methods used to reduce such redundancies and statistics regarding the occurrence of various combinations of gauge group factors and GUT groups. Statistics for both and models are presented.
118406947
GAUGE MODELS IN D DIMENSIONS
Utilizing the gauge framework, software under development at Baylor University, we explicitly construct all layer 1 weakly coupled free fermionic heterotic string (WCFFHS) gauge models up to order 32 in four to ten large spacetime dimensions. These gauge models are well suited to large scale systematic surveys and, while they offer little phenomenologically, are useful for understanding the structure of the WCFFHS region of the string landscape. Herein, we present the gauge groups statistics for this swath of the landscape for both supersymmetric and non-supersymmetric models.
73360743
Initial Systematic Investigations of the Landscape of Low-Layer NAHE Variation Extensions
The discovery that the number of physically consistent string vacua is on the order of 10500 has prompted several statistical studies of string phenomenology. Focusing on the Weakly Coupled Free Fermionic String formalism, we present systematic extensions of a variation on the NAHE (Nanopoulos, Antoniadis, Hagelin, Ellis) set of basis vectors. This variation is more conducive to the production of “mirrored” models, in which the observable and hidden sector gauge groups (and possibly matter content) are identical. This study is parallel to the extensions of the NAHE set itself and presents statistics related to similar model properties. Statistical coupling between specific gauge groups and spacetime supersymmetry is also examined. Finally, a model with completely mirrored gauge groups is discussed. It is found that the region of the landscape explored generates no physically realistic models due to a lack of three net chiral generations.
119287090
REDUNDANCIES IN EXPLICITLY CONSTRUCTED TEN-DIMENSIONAL HETEROTIC STRING MODELS
Using Baylor University's C++ software for construction of weakly coupled free fermionic heterotic string models, called the FF Framework, we explicitly construct the level-1 Kac–Moody ten-dimensional heterotic string models with the aim of understanding the redundancies endemic to this construction method. We show that for models in any even number of large space–time dimensions with a massless left-mover and an odd ordered right-mover, the maximal number of space–time supersymmetries are present. We show that in order to produce all of the models for a given order, different basis vectors must be built; one cannot vary only the GSO coefficients. We also show that all combinations of two order-2 basis vectors do not produce the same models as all possible single order-4 basis vectors, implying the product of the orders used in a search does not necessarily determine the models built. We also show that to build all of the D = 10 level-1 models the inputs must be: sets of single order-6 basis vectors, pairs of basis vectors with orders 3 and 2, or sets of three order-2 basis vectors.
119285051
Initial systematic investigations of the landscape of low layer NAHE extensions
The discovery that the number of physically consistent string vacua is on the order of 10500 has prompted several statistical studies of string phenomenology. Contained here is one such study that focuses on the Weakly Coupled Free Fermionic Heterotic String (WCFFHS) formalism. Presented are systematic extensions of the well-known NAHE (Nanopoulos, Antoniadis, Hagelin, Ellis) set of basis vectors, which have been shown to produce phenomenologically realistic models. Statistics related to the number of U(1)’s, the specific gauge groups and their factors, non-Abelian singlets, and spacetime supersymmetries (ST SUSYs) are discussed for the full range of models produced. These findings are compared with prior results of other large-scale investigations. Statistical coupling between the gauge groups and the number of ST SUSYs is also discussed. In particular, for order-3 extensions there is a correlation between the appearance of exceptional groups and enhanced ST SUSY. Also discussed are some three-generation GUT models found among the data sets. These models are unique because they come from basis vectors which still have a geometric interpretation—there are no “rank cuts” in these models.
15124605
Angular Momentum on the Lattice: The Case of Non-Zero Linear Momentum
The irreducible representations (IRs) of the double cover of the Euclidean group with parity in three dimensions are subduced to the corresponding cubic space group. The reduction of these representations gives the mapping of continuum angular momentum states to the lattice in the case of non-zero linear momentum. The continuous states correspond to lattice states with the same momentum and continuum rotational quantum numbers decompose into those of the IRs of the little group of the momentum vector on the lattice. The inverse mapping indicates degeneracies that will appear between levels of different lattice IRs in the continuum limit, recovering the continuum angular momentum multiplets. An example of this inverse mapping is given for the case of the “moving” isotropic harmonic oscillator.
73695272
The Cartan formalism in field theory
We consider a generalisation to field theory of the symplectic geometric approach to particle mechanics. This involves the definition of spacetime models; space and time as separate entities being taken as the primitive elements of the theory. Dynamical covariance and the CPT transformation of the Maxwell-Dirac and Maxwell-Schrodinger fields can then be discussed within the same formalism. A novel matrix formulation of the Schrodinger equation emerges which is a direct limit from the Dirac field.
1796910
First direct limits on lightly ionizing particles with electric charge less than e/6.
While the standard model of particle physics does not include free particles with fractional charge, experimental searches have not ruled out their existence. We report results from the Cryogenic Dark Matter Search (CDMS II) experiment that give the first direct-detection limits for cosmogenically produced relativistic particles with electric charge lower than e/6. A search for tracks in the six stacked detectors of each of two of the CDMS II towers finds no candidates, thereby excluding new parameter space for particles with electric charges between e/6 and e/200.
30892273
Silicon detector results from the first five-tower run of CDMS II
We report results of a search for weakly interacting massive particles (WIMPs) with the Si detectors of the CDMS II experiment. This report describes a blind analysis of the first data taken with CDMS II’s full complement of detectors in 2006–2007; results from this exposure using the Ge detectors have already been presented. We observed no candidate WIMP-scattering events in an exposure of 55.9 kg-days before analysis cuts, with an expected background of ∼1.1 events. The exposure of this analysis is equivalent to 10.3 kg-days over a recoil energy range of 7–100 keV for an ideal Si detector and a WIMP mass of 10  GeV/c^2. These data set an upper limit of 1.7×10^(-41)  cm^2 on the WIMP-nucleon spin-independent cross section of a 10  GeV/c^2 WIMP. These data exclude parameter space for spin-independent WIMP-nucleon elastic scattering that is relevant to recent searches for low-mass WIMPs.
6851820
The Effect of Reduced Spatial Symmetries on Lattice States: Results for Non-zero Linear Momentum
The irreducible representations of the cubic space group are described and used to determine the mapping of continuum states to lattice states with non-zero linear momentum. The Clebsch-Gordan decomposition is calculated from the character table for the cubic space group. These results are used to identify multiparticle states which appear in the hadron spectrum on the lattice.