Braid Group, Gauge Invariance and Topological Order

Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce automorphisms of the braid group, giving rise to a unified algebraic structure that characterizes the ground-state subspace and fractionally charged, anyonic quasiparticles. Minimal ground state degeneracy is derived without assuming any relation between quasiparticle charge and statistics. We also point out that noncommutativity between large gauge transformations is essential for the topological order in the fractional quantum Hall effect.Comment: 5pages, 2 figures; reference adde

A generalized structure of Bell inequalities for bipartite arbitrary dimensional systems

We propose a generalized structure of Bell inequalities for arbitrary d-dimensional bipartite systems, which includes the existing two types of Bell inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev. Lett. 88, 040404 (2002)] and Son-Lee-Kim [Phys. Rev. Lett. 96, 060406 (2006)]. We analyze Bell inequalities in terms of correlation functions and joint probabilities, and show that the coefficients of correlation functions and those of joint probabilities are in Fourier transform relations. We finally show that the coefficients in the generalized structure determine the characteristics of quantum violation and tightness.Comment: 6 pages, 1 figur

Grand Unified Yukawa Matrix Ansatz: The Standard Model Fermion Mass, Quark Mixing and CP Violation Parameters

We propose a new mass matrix ansatz: At the grand unified (GU) scale, the standard model (SM) Yukawa coupling matrix elements are integer powers of the square root of the GU gauge coupling constant \varepsilon \equiv \sqrt{\alpha_{\text{GU}}}, multiplied by order unity random complex numbers. It relates the hierarchy of the SM ermion masses and quark mixings to the gauge coupling constants, greatly reducing the SM parameters, and can give good fitting results of the SM fermion mass, quark mixing and CP violation parameters. This is a neat but very effective ansatz.Comment: 4 pages (two columns), by REVTeX 4, 2 tables, no figures, version for publication in CP

Superspace Formulation in a Three-Algebra Approach to D=3, N=4,5 Superconformal Chern-Simons Matter Theories

We present a superspace formulation of the D=3, N=4,5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action, and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new super-potential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4,5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be rederived in our 3-algebra approach. All known N=4,5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie-algebra realization of symplectic 3-algebras.Comment: 37 pages, minor changes, published in PR

Flavor Evolution of the Neutronization Neutrino Burst from an O-Ne-Mg Core-Collapse Supernova

We present results of 3-neutrino flavor evolution simulations for the neutronization burst from an O-Ne-Mg core-collapse supernova. We find that nonlinear neutrino self-coupling engineers a single spectral feature of stepwise conversion in the inverted neutrino mass hierarchy case and in the normal mass hierarchy case, a superposition of two such features corresponding to the vacuum neutrino mass-squared differences associated with solar and atmospheric neutrino oscillations. These neutrino spectral features offer a unique potential probe of the conditions in the supernova environment and may allow us to distinguish between O-Ne-Mg and Fe core-collapse supernovae.Comment: 4 pages, 2 figures. Version accepted by PR

A linear theory for control of non-linear stochastic systems

We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of temperature. The path integral displays symmetry breaking and there exist a critical noise value that separates regimes where optimal control yields qualitatively different solutions. The path integral can be computed efficiently by Monte Carlo integration or by Laplace approximation, and can therefore be used to solve high dimensional stochastic control problems.Comment: 5 pages, 3 figures. Accepted to PR

Neutrino Mass Hierarchy and Stepwise Spectral Swapping of Supernova Neutrino Flavors

We examine a phenomenon recently predicted by numerical simulations of supernova neutrino flavor evolution: the swapping of supernova $\nu_e$ and $\nu_{\mu,\tau}$ energy spectra below (above) energy \EC for the normal (inverted) neutrino mass hierarchy. We present the results of large-scale numerical calculations which show that in the normal neutrino mass hierarchy case, \EC decreases as the assumed $\nu_e\rightleftharpoons\nu_{\mu,\tau}$ effective $2\times 2$ vacuum mixing angle ($\simeq \theta_{1 3}$) is decreased. However, these calculations also indicate that \EC is essentially independent of the vacuum mixing angle in the inverted neutrino mass hierarchy case. With a good neutrino signal from a future Galactic supernova, the above results could be used to determine the neutrino mass hierarchy even if $\theta_{13}$ is too small to be detected in terrestrial neutrino oscillation experiments.Comment: 4 pages, 2 figures. Version accepted by PR