Showing papers on "Symmetry (physics) published in 2007"

The analytic Bethe ansatz for a chain with centrally extended su(2|2) symmetry

Abstract: We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2, 2|4) symmetry. These chains have their origin in the planar anti-de Sitter/conformal field theory correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended su(2|2). These results are applied in the construction and investigation of an interesting S-matrix with su(2|2) symmetry. In particular, they enable a remarkably simple proof of the Yang-Baxter relation. We also show the equivalence of the S- matrix to Shastry's R-matrix and thus uncover a hidden supersymmetry in the integrable structure of the Hubbard model. We then construct eigenvalues of the corresponding transfer matrix in order to formulate an analytic Bethe ansatz. Finally, the form of transfer matrix eigenvalues for models with psu(2, 2|4) symmetry is sketched.

Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

Abstract: The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an Abelian ideal of supertranslations. The associated charge algebra is shown to admit a non-trivial classical central extension of Virasoro type closely related to that of the anti-de Sitter case.

Electron fractionalization in two-dimensional graphenelike structures.

Abstract: Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.

Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry

Abstract: Geostatistical approaches to modeling spatio-temporal data rely on parametric covariance models and rather stringent assumptions, such as stationarity, separability and full symmetry. This paper reviews recent advances in the literature on space-time covariance functions in light of the aforementioned notions, which are illustrated using wind data from Ireland. Experiments with time-forward kriging predictors suggest that the use of more complex and more realistic covariance models results in improved predictive performance.

Near-horizon symmetries of extremal black holes

Abstract: Recent work has demonstrated an attractor mechanism for extremal rotating black holes subject to the assumption of a near-horizon SO(2,1) symmetry. We prove the existence of this symmetry for any extremal black hole with the same number of rotational symmetries as known four and five dimensional solutions (including black rings). The result is valid for a general two-derivative theory of gravity coupled to abelian vectors and uncharged scalars, allowing for a non-trivial scalar potential. We prove that it remains valid in the presence of higher-derivative corrections. We show that SO(2,1)-symmetric near-horizon solutions can be analytically continued to give SU(2)-symmetric black hole solutions. For example, the near-horizon limit of an extremal 5D Myers-Perry black hole is related by analytic continuation to a non-extremal cohomogeneity-1 Myers-Perry solution.

Particle-hole symmetry and the nu=5/2 quantum Hall state.

Abstract: We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau-level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau-level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau-level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

Abstract: Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.

An Exact SU(2) Symmetry and Persistent Spin Helix ina Spin-orbit Coupled System

Abstract: Spin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constant (the ReD model), and for the [110] Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions, and is generated by operators whose wavevector depends on the coupling strength. It renders the spin lifetime infinite at this wavevector, giving rise to a Persistent Spin Helix (PSH). We obtain the spin fluctuation dynamics at, and away, from the symmetry point, and suggest experiments to observe the PSH.

Minkowski space structure of the Higgs potential in 2HDM

Abstract: The Higgs potential of 2HDM keeps its generic form under the group of transformation $GL(2,C)$, which is larger than the usually considered reparametrization group $SU(2)$. This reparametrization symmetry induces the Minkowski space structure in the orbit space of 2HDM. Exploiting this property, we present a geometric analysis of the number and properties of stationary points of the most general 2HDM potential. In particular, we prove that charge-breaking and neutral vacua never coexist in 2HDM and establish conditions when the most general explicitly $CP$-conserving Higgs potential has spontaneously $CP$-violating minima. We also define the prototypical model of a given 2HDM, which has six free parameters less than the original one but still contains all the essential physics. Our analysis avoids manipulation with high-order algebraic equations.

Volume independence in large Nc QCD-like gauge theories

Abstract: Volume independence in large Nc gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. A natural generalization concerns volume independence in ``theory space'' of quiver gauge theories. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large Nc orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large Nc ``orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large Nc equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, such as QCD(Adj), are much easier to study (analytically or numerically) in small volume, this equivalence should allow greater understanding of large Nc QCD in infinite volume.

Density dependence of the symmetry energy and the nuclear equation of state: A dynamical and statistical model perspective

Abstract: The density dependence of the symmetry energy in the equation of state of isospin asymmetric nuclear matter is of significant importance for studying the structure of systems as diverse as the neutron-rich nuclei and the neutron stars. A number of reactions using the dynamical and the statistical models of multifragmentation, and the experimental isoscaling observable, are studied to extract information on the density dependence of the symmetry energy. It is observed that the dynamical and the statistical model calculations give consistent results assuming the sequential decay effect in dynamical model to be small. A comparison with several other independent studies is also made to obtain important constraints on the form of the density dependence of the symmetry energy. The comparison rules out an extremely ``stiff'' and ``soft'' forms of the density dependence of the symmetry energy with important implications for astrophysical and nuclear physics studies.

Coupled-mode theory for general free-space resonant scattering of waves

Abstract: We present a universal coupled-mode-theory treatment of free-space scattering of waves from resonant objects. The range of applicability of the presented approach is fairly broad: it can be used for almost any linear wave system, as long as the resonant scatterer has either three-dimensional (3D) spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the resonant wavelength of the incident wave. The presented framework, while being intuitive and analytically simple, can nevertheless provide quantitatively very accurate modeling of scattering cross sections, absorption cross sections, and many other quantities of interest. We illustrate this approach by showing how it applies to the particular examples of scattering of light from spherically symmetric resonant objects and atoms, and scattering of neutrons off nuclei.

Spectral properties of locally correlated electrons in a BCS superconductor

Abstract: We present a detailed study of the spectral properties of a locally correlated site embedded in a BCS superconducting medium. To this end the Anderson impurity model with superconducting bath is analysed by numerical renormalisation group (NRG) calculations. We calculate one and two-particle dynamic response function to elucidate the spectral excitation and the nature of the ground state for different parameter regimes with and without particle-hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameters. We also present phase diagrams for the different ground state parameter regimes. This work is also relevant for dynamical mean field theory extensions with superconducting symmetry breaking.

Particle-Number Projection and the Density Functional Theory

Abstract: In the framework of the density functional theory for superconductors, we study the restoration of the particle-number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed. Both are related to the fact that neither the many-body Hamiltonian nor the wave function of the system appear explicitly in the density functional theory. Similar obstacles are encountered in self-consistent theories utilizing density-dependent effective interactions.

Hidden Symmetries of Higher-Dimensional Rotating Black Holes

Abstract: We demonstrate that the rotating black holes in an arbitrary number of dimensions and without any restrictions on their rotation parameters possess the same hidden symmetry as the four-dimensional Kerr metric. Namely, besides the spacetime symmetries generated by the Killing vectors they also admit the (antisymmetric) Killing-Yano and symmetric Killing tensors.

Spectral properties of locally correlated electrons in a Bardeen–Cooper–Schrieffer superconductor

Abstract: We present a detailed study of the spectral properties of a locally correlated site embedded in a Bardeen–Cooper–Schrieffer (BCS) superconducting medium. To this end the Anderson impurity model with a superconducting bath is analysed by means of numerical renormalization group calculations. We calculate one-and two-particle dynamic response functions to elucidate the spectral excitations and the nature of the ground state for different parameter regimes with and without particle–hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameters. We present phase diagrams for the different ground state parameter regimes. This work is also relevant for dynamical mean field theory extensions with superconducting symmetry breaking.

Simple model of direct gauge mediation of metastable supersymmetry breaking

Abstract: We construct a model of direct gauge mediation of metastable supersymmetry breaking by simply deforming the Intriligator, Seiberg, and Shih model in terms of a dual meson superpotential mass term. No extra matter field is introduced. The deformation explicitly breaks a $U(1{)}_{R}$ symmetry and pseudomoduli have a nonzero VEV at one-loop. Our metastable supersymmetry breaking vacuum turns out to be sufficiently long-lived. By gauging a subgroup of flavor symmetry, our model can directly couple to the standard model, which leads to nonvanishing gaugino mass generation. It is also shown that our model can evade the Landau pole problem. We show the parameters in the supersymmetry breaking sector are phenomenologically constrained.

Symmetry energy at subnuclear densities and nuclei in neutron star crusts

Abstract: Department of Materials Science, Kochi University, Akebono-cho, Kochi 780-8520, Japan(Dated: February 9, 2008)We examine how the properties of inhomogeneous nuclear matter at subnuclear densities dependon the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculatethe size and shape of nuclei in neutron star matter at zero temperature in a way dependent onthe density dependence of the symmetry energy. We find that for smaller symmetry energy atsubnuclear densities, corresponding to larger density symmetry coefficient L, the charge number ofnuclei is smaller, and the critical density at which matter with nuclei or bubbles becomes uniform islower. The decrease in the charge number is associated with the dependence of the surface tensionon the nuclear density and the density of a sea of neutrons, while the decrease in the critical densitycan be generally understood in terms of proton clustering instability in uniform matter.

Axial Resonances in the Open and Hidden Charm Sectors

Abstract: A SU(4) flavor symmetrical Lagrangian is constructed for the interaction of the pseudo-scalar mesons with the vector mesons. SU(4) symmetry is broken to SU(3) by suppression of terms in the Lagrangian where the interaction should be driven by charmed mesons. Chiral symmetry can be restored by setting this new SU(4) symmetry-breaking parameters to zero. Unitarization in coupled channels leads to the dynamical generation of resonances. Many known axial resonances can be identified including the new controversial X(3872) and the structure found recently by Belle around 3875MeV in the hidden charm sector. Also new resonances are predicted, some of them with exotic quantum numbers.

Spontaneous lorentz breaking and massive gravity.

Abstract: Theories with an extra spin-two field coupled to gravity admit a massive phase with broken Lorentz symmetry. While the equivalence principle is respected, the Newtonian potentials are in general modified, but they may be protected by a scale symmetry of the coupling term. The gravitational waves phenomenology is quite rich: two gravitons, one massive and one massless, oscillate and propagate with distinct velocities, different from the speed of light. A time of flight difference between gravitons and photons from a common source would provide a clear signal of this theory.

Aperiodic Crystals: From Modulated Phases to Quasicrystals

Abstract: 1. Introduction 2. Description and symmetry of aperiodic crystals 3. Mathematical models 4. Structure 5. Origin and stability 6. Physical properties 7. Other topics Appendix A. Higher-dimensional space groups Appendix B. Magnetic symmetry of quasi-periodic systems