Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua

In this paper, we show that the presence of gauge fields in heterotic Calabi-Yau compacitifications causes the stabilisation of some, or all, of the complex structure moduli of the Calabi-Yau manifold while maintaining a Minkowski vacuum. Certain deformations of the Calabi-Yau complex structure, with all other moduli held fixed, can lead to the gauge bundle becoming non-holomorphic and, hence, non-supersymmetric. This leads to an F-term potential which stabilizes the corresponding complex structure moduli. We use 10- and 4-dimensional field theory arguments as well as a derivation based purely on algebraic geometry to show that this picture is indeed correct. An explicit example is presented in which a large subset of complex structure moduli is fixed. We demonstrate that this type of theory can serve as the hidden sector in heterotic vacua and can co-exist with realistic particle physics.Comment: 17 pages, Late

Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the computation depends only on a one-dimensional ray in the Kahler moduli space, it can probe slope-stability regardless of the size of h^{1,1}. Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kahler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, an efficient numerical check is proposed for determining whether or not a vector bundle is slope-stable without computing its full connection.Comment: 38 pages, 10 figure

Heterotic Line Bundle Standard Models

In a previous publication, arXiv:1106.4804, we have found 200 models from heterotic Calabi-Yau compactifications with line bundles, which lead to standard models after taking appropriate quotients by a discrete symmetry and introducing Wilson lines. In this paper, we construct the resulting standard models explicitly, compute their spectrum including Higgs multiplets, and analyze some of their basic properties. After removing redundancies we find about 400 downstairs models, each with the precise matter spectrum of the supersymmetric standard model, with one, two or three pairs of Higgs doublets and no exotics of any kind. In addition to the standard model gauge group, up to four Green-Schwarz anomalous U(1) symmetries are present in these models, which constrain the allowed operators in the four-dimensional effective supergravity. The vector bosons associated to these anomalous U(1) symmetries are massive. We explicitly compute the spectrum of allowed operators for each model and present the results, together with the defining data of the models, in a database of standard models accessible at http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/linebundlemodels/index.html. Based on these results we analyze elementary phenomenological properties. For example, for about 200 models all dimension four and five proton decay violating operators are forbidden by the additional U(1) symmetries.Comment: 55 pages, Latex, 3 pdf figure

Measuring Accuracy of Automated Parsing and Categorization Tools and Processes in Digital Investigations

This work presents a method for the measurement of the accuracy of evidential artifact extraction and categorization tasks in digital forensic investigations. Instead of focusing on the measurement of accuracy and errors in the functions of digital forensic tools, this work proposes the application of information retrieval measurement techniques that allow the incorporation of errors introduced by tools and analysis processes. This method uses a `gold standard' that is the collection of evidential objects determined by a digital investigator from suspect data with an unknown ground truth. This work proposes that the accuracy of tools and investigation processes can be evaluated compared to the derived gold standard using common precision and recall values. Two example case studies are presented showing the measurement of the accuracy of automated analysis tools as compared to an in-depth analysis by an expert. It is shown that such measurement can allow investigators to determine changes in accuracy of their processes over time, and determine if such a change is caused by their tools or knowledge.Comment: 17 pages, 2 appendices, 1 figure, 5th International Conference on Digital Forensics and Cyber Crime; Digital Forensics and Cyber Crime, pp. 147-169, 201

Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds

We systematically approach the construction of heterotic E_8 X E_8 Calabi-Yau models, based on compact Calabi-Yau three-folds arising from toric geometry and vector bundles on these manifolds. We focus on a simple class of 101 such three-folds with smooth ambient spaces, on which we perform an exhaustive scan and find all positive monad bundles with SU(N), N=3,4,5 structure groups, subject to the heterotic anomaly cancellation constraint. We find that anomaly-free positive monads exist on only 11 of these toric three-folds with a total number of bundles of about 2000. Only 21 of these models, all of them on three-folds realizable as hypersurfaces in products of projective spaces, allow for three families of quarks and leptons. We also perform a preliminary scan over the much larger class of semi-positive monads which leads to about 44000 bundles with 280 of them satisfying the three-family constraint. These 280 models provide a starting point for heterotic model building based on toric three-folds.Comment: 41 pages, 5 figures. A table modified and a table adde

Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories

A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.Comment: 52 pages, 15 figures. LaTex formatting of figures corrected in version 2

Yukawa Textures From Heterotic Stability Walls

A holomorphic vector bundle on a Calabi-Yau threefold, X, with h^{1,1}(X)>1 can have regions of its Kahler cone where it is slope-stable, that is, where the four-dimensional theory is N=1 supersymmetric, bounded by "walls of stability". On these walls the bundle becomes poly-stable, decomposing into a direct sum, and the low energy gauge group is enhanced by at least one anomalous U(1) gauge factor. In this paper, we show that these additional symmetries can strongly constrain the superpotential in the stable region, leading to non-trivial textures of Yukawa interactions and restrictions on allowed masses for vector-like pairs of matter multiplets. The Yukawa textures exhibit a hierarchy; large couplings arise on the stability wall and some suppressed interactions "grow back" off the wall, where the extended U(1) symmetries are spontaneously broken. A number of explicit examples are presented involving both one and two stability walls, with different decompositions of the bundle structure group. A three family standard-like model with no vector-like pairs is given as an example of a class of SU(4) bundles that has a naturally heavy third quark/lepton family. Finally, we present the complete set of Yukawa textures that can arise for any holomorphic bundle with one stability wall where the structure group breaks into two factors.Comment: 53 pages, 4 figures and 13 table

Quantum spin liquid states in the two dimensional kagome antiferromagnets, ZnxCu4-x(OD)6Cl2

A three-dimensional system of interacting spins typically develops static long-range order when it is cooled. If the spins are quantum (S = 1/2), however, novel quantum paramagnetic states may appear. The most highly sought state among them is the resonating valence bond (RVB) state in which every pair of neighboring quantum spins form entangled spin singlets (valence bonds) and the singlets are quantum mechanically resonating amongst all the possible highly degenerate pairing states. Here we provide experimental evidence for such quantum paramagnetic states existing in frustrated antiferromagnets, ZnxCu4-x(OD)6Cl2, where the S = 1/2 magnetic Cu2+ moments form layers of a two-dimensional kagome lattice. We find that in Cu4(OD)6Cl2, where distorted kagome planes are weakly coupled to each other, a dispersionless excitation mode appears in the magnetic excitation spectrum below ~ 20 K, whose characteristics resemble those of quantum spin singlets in a solid state, known as a valence bond solid (VBS), that breaks translational symmetry. Doping nonmagnetic Zn2+ ions reduces the distortion of the kagome lattice, and weakens the interplane coupling but also dilutes the magnetic occupancy of the kagome lattice. The VBS state is suppressed and for ZnCu3(OD)6Cl2 where the kagome planes are undistorted and 90% occupied by the Cu2+ ions, the low energy spin fluctuations in the spin liquid phase become featureless

Large-scale air mass characteristics observed over the remote tropical Pacific Ocean during March-April 1999: Results from PEM-Tropics B field experiment

Eighteen long-range flights over the Pacific Ocean between 38° S to 20° N and 166° E to 90° W were made by the NASA DC-8 aircraft during the NASA Pacific Exploratory Mission (PEM) Tropics B conducted from March 6 to April 18, 1999. Two lidar systems were flown on the DC-8 to remotely measure vertical profiles of ozone (O3), water vapor (H2O), aerosols, and clouds from near the surface to the upper troposphere along their flight track. In situ measurements of a wide range of gases and aerosols were made on the DC-8 for comprehensive characterization of the air and for correlation with the lidar remote measurements. The transition from northeasterly flow of Northern Hemispheric (NH) air on the northern side of the Intertropical Convergence Zone (ITCZ) to generally easterly flow of Southern Hemispheric (SH) air south of the ITCZ was accompanied by a significant decrease in O3, carbon monoxide, hydrocarbons, and aerosols and an increase in H2O. Trajectory analyses indicate that air north of the ITCZ came from Asia and/or the United States, while the air south of the ITCZ had a long residence time over the Pacific, perhaps originating over South America several weeks earlier. Air south of the South Pacific Convergence Zone (SPCZ) came rapidly from the west originating over Australia or Africa. This air had enhanced O3 and aerosols and an associated decrease in H2O. Average latitudinal and longitudinal distributions of O3 and H2O were constructed from the remote and in situ O3 and H2O data, and these distributions are compared with results from PEM-Tropics A conducted in August-October 1996. During PEM-Tropics B, low O3 air was found in the SH across the entire Pacific Basin at low latitudes. This was in strong contrast to the photochemically enhanced O3 levels found across the central and eastern Pacific low latitudes during PEM-Tropics A. Nine air mass types were identified for PEM-Tropics B based on their O3, aerosols, clouds, and potential vorticity characteristics. The data from each flight were binned by altitude according to air mass type, and these results showed the relative observational frequency of the different air masses as a function of altitude in seven regions over the Pacific. The average chemical composition of the major air mass types was determined from in situ measurements in the NH and SH, and these results provided insight into the origin, lifetime, and chemistry of the air in these regions. Copyright 2001 by the American Geophysical Union