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Axially-symmetric sphaleron solutions of the Skyrme model
Get PDFStatic axially symmetric sphaleron-type solutions describing chains of interpolating Skyrmion–anti-Skyrmions have been constructed numerically. The configurations are characterized by two integers n and m, where ±n are the winding numbers of the constituent Skyrmion and anti-Skyrmion and the second integer m defines type of the solution, it has zero topological charge for even m and for odd values of m the Skyrmion–anti-Skyrmion chain has topological charge n. For the vanishing mass term we confirm the existence of such chain solutions for winding number |n| ≥ 2. The similarity with monopole–anti-monopole pairs is highlighted
New Chern-Simons densitites in both odd and even dimensions
Get PDFAfter reviewing briefly the dimensional reduction of Chern–Pontryagin densitie, we define new Chern–Simons densities expressed in terms of Yang-Mills and Higgs fields. These are defined in all dimensions, including in even dimensional spacetimes. They are constructed by subjecting the dimensionally reduced Chern–Pontryagin densites to further descent by two steps
Toric elliptic fibrations and F-theory compactifications
Get PDFThe 102,581 flat toric elliptic fibrations over P^2 are identified among the Calabi-Yau hypersurfaces that arise from the 473,800,776 reflexive 4-dimensional polytopes. In order to analyze their elliptic fibration structure, we describe the precise relation between the lattice polytope and the elliptic fibration. The fiber-divisor-graph is introduced as a way to visualize the embedding of the Kodaira fibers in the ambient toric fiber. In particular in the case of non-split discriminant components, this description is far more accurate than previous studies. The discriminant locus and Kodaira fibers of all 102,581 elliptic fibrations are computed. The maximal gauge group is SU(27), which would naively be in contradiction with 6-dimensional anomaly cancellation
The MSSM spectrum from (0,2)-deformations of the heterotic standard embedding
Get PDFWe construct supersymmetric compactifications of E_8 × E_8 heterotic string theory which realise exactly the massless spectrum of the Minimal Supersymmetric Standard Model (MSSM) at low energies. The starting point is the standard embedding on a Calabi-Yau threefold which has Hodge numbers (h^1,1 , h^2,1 ) = (1, 4) and fundamental group Z_12 , which gives an E_6 grand unified theory with three net chiral generations. The gauge symmetry is then broken to that of the standard model by a combination of discrete Wilson lines and continuous deformation of the gauge bundle. On eight distinct branches of the moduli space, we find stable bundles with appropriate cohomology groups to give exactly the massless spectrum of the MSSM
Equivariant dimensional reduction and quiver gauge theories
Get PDFWe review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills-Higgs-Dirac theories with dynamical mass generation and exactly massless chiral fermions
Asymptotically Flat, Stable Black Hole Solutions in Einstein–Yang-Mills–Chern-Simons Theory
Get PDFWe construct finite mass, asymptotically flat black hole solutions in d = 5 Einstein– Yang-Mills–Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. In addition a solution in closed form describing an extremal black hole with non-Abelian hair is found for a special value of the Chern-Simons coupling constant
AdS/QHE: towards a holographic description of quantum Hall experiments
Get PDFTransitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semi-circle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the DC ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero DC conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semi-circle transitions between them. The model can be regarded as a strongly coupled analog of the old ‘composite boson’ picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model. In particular, the model indicates the value 2/5 for low-temperature scaling exponents for transitions among quantum Hall plateaux, in agreement with the measured value 0.42 ± 0.04
Analytical computation of the lattice rotations induced by 3D dislocation loops
Get PDFThis paper presents the derivation of expressions for the lattice rotations induced by a triangular dislocation loop in an isotropic, elastic medium, based on the classical displacement field solution for a triangular dislocation loop. Using the simple example of a triangular dislocation loop with one segment of edge character, one segment of screw character and a mixed character segment, a comparison of the 3D lattice rotation fields with those predicted for straight, infinitely long 2D dislocations is made. Agreement is excellent. As an illustration of the utility of the rotation solution, the lattice rotations induced by a Frank-Read Source are studied at different stages during its evolution. The dislocation segment positions were computed using the discrete dislocation dynamics code ParaDiS. Post-processing of the lattice rotation maps in terms of lattice orientation spread reveals preferential lattice misorientation or streaking which is consistent with the single active slip system in the simulation. Streaking is a feature frequently observed in micro-diffraction measurements. The availability of the lattice rotation solution makes it possible to evaluate the lattice rotations arising from any 3D distribution of dislocation segments. This allows the computation of predicted diffraction patterns from computed dislocation substructures for direct comparison with experimental measurements. It also makes the inclusion of lattice rotations into 3D dislocation dynamics codes possible. This effect has thus far been treated as small, but was shown to be important in 2D dislocation dynamics simulations
