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Showing papers on "Symmetry (physics) published in 2013"


Journal ArticleDOI
TL;DR: This paper focuses on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle and gives a mini-review of finite group theory.
Abstract: This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A₄, S₄ and Δ(96).

849 citations


Journal ArticleDOI
TL;DR: In this paper, electric fields can break the structural inversion symmetry in bilayer 2D materials, providing a way of tuning the magnetic moment and Berry curvature of bilayer materials.
Abstract: Electric fields can break the structural inversion symmetry in bilayer 2D materials, providing a way of tuning the magnetic moment and Berry curvature. This effect can be probed directly in bilayer MoS2 using optical measurements.

555 citations


Journal ArticleDOI
TL;DR: In this article, a procedure is developed for constructing deformations of integrable σ-models which are themselves classically integrably this article and the actions correspond to a deformation of the target space geometry and include a torsion term.
Abstract: A procedure is developed for constructing deformations of integrable σ-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter σ-model introduced a few years ago by C. Klimyc´ok. In the case of the symmetric space σ-model on F/G we obtain a new one-parameter family of integrable σ-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset σ-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset σ-model which interpolates all the way to the SU(1,1)/U(1) coset σ-model.

363 citations


Journal ArticleDOI
TL;DR: The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space as mentioned in this paper, which underlies the conservation of optical helicity and is closely related to the separation of spin and orbital degrees of freedom of light.
Abstract: The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy–momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy–momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincare symmetries, examine both local and integral conserved quantities and show that only the dual electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments.

329 citations


Journal ArticleDOI
TL;DR: In this paper, a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras was described, where the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the fourdimensional theory.
Abstract: We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four-dimensional theory. Infinite chiral symmetry has far-reaching consequences for the spectral data, correlation functions, and central charges of any four-dimensional theory with ${\mathcal N}=2$ superconformal symmetry.

310 citations


Journal ArticleDOI
TL;DR: In this paper, a procedure is developed for constructing deformations of integrable sigma-models, which are themselves classically integrably. But the deformation of these models correspond to a torsion term and include a classical q-deformed Poisson-Hopf algebra.
Abstract: A procedure is developed for constructing deformations of integrable sigma-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter sigma-model introduced a few years ago by C. Klimcik. In the case of the symmetric space sigma-model on F/G we obtain a new one-parameter family of integrable sigma-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset sigma-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset sigma-model which interpolates all the way to the SU(1,1)/U(1) coset sigma-model.

304 citations


Posted Content
TL;DR: In this paper, a systematic way to construct symmetry-protected topological (SPT) states in interacting bosonic systems is presented, which allows us to identify many new SPT phases, including three bosonic versions of topological insulators in three dimensions and one in two dimensions protected by particle number conservation and time reversal symmetry.
Abstract: Symmetry protected topological (SPT) states are bulk gapped states with gapless edge excitations protected by certain symmetries. The SPT phases in free fermion systems, like topological insulators, can be classified by the K-theory. However, it is not known what SPT phases exist in general interacting systems. In this paper, we present a systematic way to construct SPT phases in interacting bosonic systems, which allows us to identify many new SPT phases, including three bosonic versions of topological insulators in three dimension and one in two dimension protected by particle number conservation and time reversal symmetry. Just as group theory allows us to construct 230 crystal structures in 3D, we find that group cohomology theory allows us to construct different interacting bosonic SPT phases in any dimensions and for any symmetry groups. In particular, we are going to show how topological terms in the path integral description of the system can be constructed from nontrivial group cohomology classes, giving rise to exactly soluble Hamiltonians, explicit ground state wave functions and symmetry protected gapless edge excitations.

245 citations


Journal ArticleDOI
TL;DR: In this article, a general principle dubbed $c$ extremization was proposed to determine the exact symmetry of a two-dimensional unitary superconformal field theory with super-Yang-Mills supersymmetry.
Abstract: We uncover a general principle dubbed $c$ extremization, which determines the exact $R$ symmetry of a two-dimensional unitary superconformal field theory with $\mathcal{N}=(0,2)$ supersymmetry. To illustrate its utility, we study superconformal theories obtained by twisted compactifications of four-dimensional $\mathcal{N}=4$ super--Yang-Mills theory on Riemann surfaces and construct their gravity duals.

220 citations


Journal ArticleDOI
TL;DR: In this paper, the chiral ring and moduli space on the Coulomb branch of an N = 4 superconformal field theory in 2+1 dimensions were identified.
Abstract: This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an N = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional N = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.

201 citations


Journal ArticleDOI
TL;DR: The first example of a nontrivial higher spin theory in three-dimensional flat space is presented, and the asymptotic symmetry algebra is a (centrally extended) higher spin generalization of the Bondi-Metzner-Sachs algebra, which is described in detail.
Abstract: We present the first example of a nontrivial higher spin theory in three-dimensional flat space. We propose flat-space boundary conditions and prove their consistency for this theory. We find that the asymptotic symmetry algebra is a (centrally extended) higher spin generalization of the Bondi-Metzner-Sachs algebra, which we describe in detail. We also address higher spin analogues of flat space cosmology solutions and possible generalizations.

175 citations


Journal ArticleDOI
TL;DR: In this paper, all correlation functions of conserved currents of the CFT that is dual to unbroken Vasiliev theory are found as invariants of higher-spin symmetry in the bulk of AdS.
Abstract: All correlation functions of conserved currents of the CFT that is dual to unbroken Vasiliev theory are found as invariants of higher-spin symmetry in the bulk of AdS. The conformal and higher-spin symmetry of the correlators as well as the conservation of currents are manifest, which also provides a direct link between the Maldacena-Zhiboedov result and higher-spin symmetries. Our method is in the spirit of AdS/CFT, though we never take any boundary limit or compute any bulk integrals. Boundary-to-bulk propagators are shown to exhibit an algebraic structure, living at the boundary of SpH(4), semidirect product of Sp(4) and the Heisenberg group. N-point correlation function is given by a product of N elements.

Journal ArticleDOI
TL;DR: The density-independent smoothed particle hydrodynamics (DISPH) as mentioned in this paper is a new formulation of SPH that does not require the differentiability of density at the contact discontinuity, instead of the mass density, it adopts the internal energy density (pressure) and its arbitrary function, which are smoothed quantities as the volume element used for the kernel integration.
Abstract: The standard formulation of the smoothed particle hydrodynamics (SPH) assumes that the local density distribution is differentiable. This assumption is used to derive the spatial derivatives of other quantities. However, this assumption breaks down at the contact discontinuity. At the contact discontinuity, the density of the low-density side is overestimated while that of the high-density side is underestimated. As a result, the pressure of the low-density (high-density) side is overestimated (underestimated). Thus, unphysical repulsive force appears at the contact discontinuity, resulting in the effective surface tension. This tension suppresses fluid instabilities. In this paper, we present a new formulation of SPH, which does not require the differentiability of density. Instead of the mass density, we adopt the internal energy density (pressure) and its arbitrary function, which are smoothed quantities at the contact discontinuity, as the volume element used for the kernel integration. We call this new formulation density-independent SPH (DISPH). It handles the contact discontinuity without numerical problems. The results of standard tests such as the shock tube, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, point-like explosion, and blob tests are all very favorable to DISPH. We conclude that DISPH solved most of the known difficulties of the standard SPH, without introducing additional numerical diffusion or breaking the exact force symmetry or energy conservation. Our new SPH includes the formulation proposed by Ritchie & Thomas as a special case. Our formulation can be extended to handle a non-ideal gas easily.

Journal ArticleDOI
TL;DR: In this paper, a fully-gauge and o(d, 2 ) -covariant approach to boundary values of AdS d + 1 gauge fields is presented.

Journal ArticleDOI
TL;DR: It is shown that this equation can be reduced to an equation which is related to the Erdelyi–Kober fractional derivative, and this method can be applied to other nonlinear fractional partial differential equations.

Journal ArticleDOI
TL;DR: In this paper, all possible scaling IR asymptotics in homogeneous, translation invariant holographic phases preserving or breaking a U(1) symmetry in the IR are classified scale invariant geometries where the scalar extremizes its effective potential are distinguished from hyperscaling violating the U( 1) symmetry, and the generic global IR picture emerging is that of quantum critical lines, separated by quantum critical points which correspond to the scale-invariant solutions with a constant scalar.
Abstract: All possible scaling IR asymptotics in homogeneous, translation invariant holographic phases preserving or breaking a U(1) symmetry in the IR are classified Scale invariant geometries where the scalar extremizes its effective potential are distinguished from hyperscaling violating geometries where the scalar runs logarithmically It is shown that the general critical saddle-point solutions are characterized by three critical exponents (θ, z, ζ) Both exact solutions as well as leading behaviors are exhibited Using them, neutral or charged geometries realizing both fractionalized or cohesive phases are found The generic global IR picture emerging is that of quantum critical lines, separated by quantum critical points which correspond to the scale invariant solutions with a constant scalar

Journal ArticleDOI
TL;DR: In this article, a model of chaotic inflation based on the theory of a scalar field with potential λ 4 perfectly matches the observational data if one adds to it a tiny non-minimal coupling to gravity with ξ 0.002.
Abstract: A model of chaotic inflation based on the theory of a scalar field with potential λ4 perfectly matches the observational data if one adds to it a tiny non-minimal coupling to gravity with ξ0.002. We describe embedding of this model into the superconformal theory with spontaneous breaking of superconformal symmetry, and into supergravity. A model with small ξ is technically natural: setting the small parameter ξ to zero leads to a point of enhanced symmetry in the underlying superconformal theory.

Journal ArticleDOI
TL;DR: In this article, a review article about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry is presented, with a focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle.
Abstract: This is a review article about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A4, S4 and Delta(96).

Journal ArticleDOI
TL;DR: In this article, it was shown that the tensor transformation rule for finite coordinate transformations is consistent with the standard exponential map and compatible with the full covariance of the derivatives and curvatures after projectors are properly imposed.
Abstract: As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a ‘gauge orbit’ in the coordinate space. The diffeomorphism symmetry then implies an invariance under arbitrary reparametrizations of the gauge orbits. Within this generalized sense of diffeomorphism, we show that a recently proposed tensorial transformation rule for finite coordinate transformations is actually (i) consistent with the standard exponential map, and further (ii) compatible with the full covariance of the ‘semi-covariant’ derivatives and curvatures after projectors are properly imposed.

Journal ArticleDOI
TL;DR: In this article, the authors consider a general situation of single field inflation and show that the three point function involving two scalar modes and one tensor mode is uniquely determined, up to small corrections, by the conformal symmetries.
Abstract: During inflation, spacetime is approximately described by de Sitter space which is conformally invariant with the symmetry group SO(1,4). This symmetry can significantly constrain the quantum perturbations which arise in the inflationary epoch. We consider a general situation of single field inflation and show that the three point function involving two scalar modes and one tensor mode is uniquely determined, up to small corrections, by the conformal symmetries. Special conformal transformations play an important role in our analysis. Our result applies only to models where the inflaton sector also approximately preserves the full conformal group and shows that this three point function is a good way to test if special conformal invariance was preserved during inflation.

Journal ArticleDOI
TL;DR: It is shown that even when the nonlinearity is insufficient to induce a transition from broken to full PT symmetry, still, the wave functions neither decay nor diverge, despite the fact that the system has a complex eigenvalue spectrum.
Abstract: We study the effect of nonlinearity on systems with periodic parity-time ($PT$) symmetry, and show that nonlinearity can transform the system from broken to full $PT$ symmetry and vice versa. Furthermore, we show that even when the nonlinearity is insufficient to induce a transition from broken to full $PT$ symmetry, still, the wave functions neither decay nor diverge, despite the fact that the system has a complex eigenvalue spectrum. Rather, the amplitudes of the wavefunctions oscillate around the transition point. Our results apply to a wide variety of systems in optics and beyond.

Journal Article
TL;DR: In this paper, the magnetic field of a permanent magnet is calculated analytically for different geometries, such as a sphere, cone, cylinder, ring and rectangular prism.
Abstract: The magnetic field of a permanent magnet is calculated analytically for different geometries. The cases of a sphere, cone, cylinder, ring and rectangular prism are studied. The calculation on the axis of symmetry is presented in every case. For magnets with cylindrical symmetry, we propose an approach based on an expansion in Legendre polynomials to obtain the field at points off the axis. The case of a cylinder magnet was analyzed with this method by calculating the force between two magnets of this shape. Experimental results are presented too, showing a nice agreement with theory.

Journal ArticleDOI
TL;DR: In this paper, the bispectrum of primordial curvature perturbations in the squeezed configuration, in which one wavenumber, k3, is much smaller than the other two, k 3 > c 0, was measured.
Abstract: The bispectrum of primordial curvature perturbations in the squeezed configuration, in which one wavenumber, k3, is much smaller than the other two, k3 > c0. A cosmic-variance-limited experiment measuring temperature anisotropy of the cosmic microwave background up to lmax = 2000 is able to measure these coefficients down to δc0 = 4.4, δc1 = 61, and δc2 = 13 (68% CL). We also find that c0 and c1, and c0 and c2, are nearly uncorrelated. Measurements of these coefficients will open up a new window into the physics of inflation such as the existence of vector fields during inflation or non-trivial symmetry structure of inflaton fields. Finally, we show that the original form of the Suyama-Yamaguchi inequality does not apply to the case involving higher-spin fields, but a generalized form does.

Journal ArticleDOI
TL;DR: In this article, an improved version of the Galilean Genesis model is proposed to address the problem of superluminality, which demotes the full conformal group to Poincare symmetry and dilations, supplemented with approximate galilean shift invariance in the UV and at small field values.
Abstract: We put forward an improved version of the Galilean Genesis model that addresses the problem of superluminality. We demote the full conformal group to Poincare symmetry and dilations, supplemented with approximate galilean shift invariance in the UV and at small field values. In this way fluctuations around the NEC-violating cosmological background are made substantially subluminal, and superluminality cannot be reached by any small change of the solution, in contrast with the original model. Dilation invariance still protects the scale-invariance of correlation functions of a massless test scalar — which is the source of the observed cosmological fluctuations — but the explicit breaking of the conformal group can be potentially observed in higher-order correlators. We also highlight a subtlety in matching the NEC-violating phase with the standard cosmological evolution, and discuss the possible couplings of the Galileon to gravity.

Journal ArticleDOI
Christoph Luhn1
TL;DR: In this article, the S4 family symmetry of the neutrino sector is broken to a residual Z2 symmetry and the solar mixing angle is decreased compared to its tri-bimaximal value by about 1

Journal ArticleDOI
TL;DR: Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified and detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.
Abstract: Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.

Journal ArticleDOI
TL;DR: In this article, the authors obtained predictions of lepton mixing parameters for direct models based on Δ ( 6 n 2 ) family symmetry groups for arbitrarily large n in which the full Klein symmetry is identified as a subgroup of the family symmetry.

Journal ArticleDOI
TL;DR: These conditions can be applied to any particle with cylindrical symmetry, not only to spherical particles as the original Kerker conditions were derived for, and find applications in the field of metamaterials, where new materials with directional scattering are being explored.
Abstract: We unveil the relationship between two anomalous scattering processes known as Kerker conditions and the duality symmetry of Maxwell equations. We generalize these conditions and show that they can be applied to any particle with cylindrical symmetry, not only to spherical particles as the original Kerker conditions were derived for. We also explain the role of the optical helicity in these scattering processes. Our results find applications in the field of metamaterials, where new materials with directional scattering are being explored.

Journal ArticleDOI
TL;DR: In this paper, a unified introduction to the symmetry analysis and its action on the motion in one-dimensional periodic, both in time and space, potentials is presented. And the analysis is further generalized to quasi-periodic drivings, higher space dimensions, and quantum dynamics.
Abstract: Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space-time symmetries of the corresponding equations of motion. A systematic analysis of these symmetries uncovers the conditions necessary for obtaining directed transport. In this work we give a unified introduction into the symmetry analysis and demonstrate its action on the motion in one-dimensional periodic, both in time and space, potentials. We further generalize the analysis to quasi-periodic drivings, higher space dimensions, and quantum dynamics. Recent experimental results on the transport of cold and ultracold atomic ensembles in ac-driven optical potentials are reviewed as illustrations of theoretical considerations.

Journal ArticleDOI
TL;DR: In this article, a tensor transformation rule for finite coordinate transformations is shown to be consistent with the standard exponential map and compatible with the full covariance of the derivatives and curvatures after projectors are properly imposed.
Abstract: As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a `gauge orbit' in the coordinate space. The diffeomorphism symmetry then implies an invariance under arbitrary reparametrizations of the gauge orbits. Within this generalized sense of diffeomorphism, we show that a recently proposed tensorial transformation rule for finite coordinate transformations is actually (i) consistent with the standard exponential map, and further (ii) compatible with the full covariance of the `semi-covariant' derivatives and curvatures after projectors are properly imposed.

Journal ArticleDOI
TL;DR: In this paper, the existence and uniqueness of limit cycles for continuous piecewise-linear differential systems with three linearity zones without symmetry and having one equilibrium point in the central region is shown.
Abstract: Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter proofs of known results.