Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)

The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(\infty) and of the Lie superalgebra osp(1|\infty). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labelled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. We also present expressions for the character of the Fock space representations

Gauging Nonlinear Supersymmetry

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local supersymmetries. The resulting action is an invariant form of the Einstein-Hilbert action, which in addition to the gravitational vierbein, also includes a massive gravitino field. Invariant interactions with matter and gauge fields are also constructed. The effective Lagrangian describing processes involving the emission or absorption of a single light gravitino is analyzed.Comment: 20 pages, no figure

Production of π0ρ0\pi^0\rho^0 pair in electron-positron annihilation in the Nambu-Jona-Lasinio model

The process $e^+e^- \to \pi^0\rho$ is described in the framework of the expanded NJL model in the energy region from 0.9 GeV to 1.5 GeV. The contribution of intermediate state with vector mesons $\omega(782), \,\,\phi(1020)$, and $\omega'(1420)$, where $\omega'$ is the first radial excitation of $\omega$ - meson was taken into account. Results obtained are in satisfactory agreement with experimental data.Comment: 5 pages, 1 figure, 1 tabl

Contributions of semi-hadronic states Pγ;Sγ,π+π−γP\gamma;S\gamma, \pi^+\pi^-\gamma to amm of muon, in frames of Nambu-Jona-Lasinio model

We calculate the contribution of semi-hadronic states with pseudoscalar $P=\pi^0, \eta$ and scalar ($\sigma$(550))meson accompanied with real photon as an intermediate state of a heavy photon to the anomalous magnetic moment of muon. We consider the intermediate states with $\pi_0$ and $\sigma$ as a hadrons in frames of Nambu-Jona-Lasinio model. The contribution of $\pi_0\gamma$ state is in agreement with results obtained in previous theoretical considerations as well as with experimental data $a_\mu^{\pi_0\gamma}\approx 4.5 \times 10^{-10}$, besides we estimate $a_{\mu}^{\eta\gamma}=0.7 \times 10^{-10}, a_{\mu}^{\sigma\gamma} \sim 1.5 \times 10^{-11}, a_{\mu}^{\pi^+\pi^-\gamma} \sim 3.2 \times 10^{-10}.$ We discass as well the LbL mechanism with $a_{\mu}^{lbl}=10.5 \cdot 10^{-10}.$Comment: 6 pages, 2 figure

N=2 supersymmetric Yang-Mills theory and the superparticle: twistor transform and kappa-symmetry

Lagrangian and Hamiltonian dynamics of de Azcarraga-Lukierski N=2 massive superparticle is considered in the framework of twistor-like Lorentz-harmonic approach. The emphasis is on the study of the interaction with external Abelian gauge superfield. The requirement of preservation of all gauge symmetries of the free model including kappa-symmetry yields correct expressions for the superfield strength constraints and determines the form of nonminimal interaction. We also show that for de Azcarraga-Lukierski N=2 massive superparticle the pullback of field strength 2-superform to the superworld line is not integrable in contrast to the massless superparticle.Comment: 16 pages, LaTe

Non-BPS Brane Dynamics And Dual Tensor Gauge Theory

The action for the long wavelength oscillations of a non-BPS p=3 brane embedded in N=1, D=5 superspace is determined by means of the coset method. The D=4 world volume Nambu-Goldstone boson of broken translation invariance and the two D=4 world volume Weyl spinor Goldstinos of the completely broken supersymmetry describe the excitations of the brane into the broken space and superspace directions. The resulting action is an invariant synthesis of the Akulov-Volkov and Nambu-Goto actions. The D=4 antisymmetric tensor gauge theory action dual to the p=3 brane action is determined.Comment: 15 pages, no figure

Topological Insulators with Inversion Symmetry

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which characterize the groundstate. In two dimensions there is a single Z_2 invariant which distinguishes the ordinary insulator from the quantum spin Hall phase. In three dimensions there are four Z_2 invariants, which distinguish the ordinary insulator from "weak" and "strong" topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the 2D quantum spin Hall phase and the 3D strong topological insulator these states are robust and are insensitive to weak disorder and interactions. In this paper we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the Z_2 invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wavefunctions at the time reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials are strong topological insulators, including the semiconducting alloy Bi_{1-x} Sb_x as well as \alpha-Sn and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.Comment: 16 pages, 7 figures; published versio