Refining the Shifted Topological Vertex

We study aspects of the refining and shifting properties of the 3d MacMahon function $\mathcal{C}_{3}(q)$ used in topological string theory and BKP hierarchy. We derive the explicit expressions of the shifted topological vertex $\mathcal{S}_{\lambda \mu \nu}(q)$ and its refined version $\mathcal{T}_{\lambda \mu \nu}(q,t)$. These vertices complete results in literature.Comment: Latex, 14 pages, 2 figures. To appear in Jour Math Phy

On Dirac Zero Modes in Hyperdiamond Model

Using the SU(5) symmetry of the 4D hyperdiamond and results on the study of 4D graphene given in "Four Dimensional Graphene" (L.B Drissi, E.H Saidi, M. Bousmina, CPM-11-01, Phys. Rev. D (2011)), we engineer a class of 4D lattice QCD fermions whose Dirac operators have two zero modes. We show that generally the zero modes of the Dirac operator in hyperdiamond fermions are captured by a tensor {\Omega}_{{\mu}}^{l} with 4\times5 complex components linking the Euclidean SO(4) vector {\mu}; and the 5-dimensional representation of SU(5). The Bori\c{c}i-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their Dirac zero modes are rederived as particular realizations of {\Omega}_{{\mu}}^{l}. Other features are also given. Keywords: Lattice QCD, Bori\c{c}i-Creutz and Karsten-Wilzeck models, 4D hyperdiamond, 4D graphene, SU(5) Symmetry.Comment: LaTex, 28 pages, To appear in Phys Rev

Graphene and Cousin Systems

Graphene is a new material that exhibits remarkable properties from both fundamental and applied issues. This is a 2D matter system whose physical and mechanical features have been approached by using tight binding model, first principle calculations based on DFT and membrane theory. Graphene as a carbon molecule has also hidden symmetries that motivated extensions in various dimensions such as chain-type configurations, that are frequently observed as the graphene bridge narrowed down to a few- or single-atom width, graphene multi-layers thought of as electric capacitors, doped graphene to gain more physical properties as well as cousin systems such as diamond and hyperdiamond. In this work, we use tight binding model ideas and field theory method as well as the hidden symmetries of the underlying crystals to study physical aspects of 2D graphene and its homologues. We also study the relation between 2D graphene with the Bori\c{c}i-Creutz fermions considered recently in literature as an adequate model to perform numerical simulations in 4D lattice QCD where the two Dirac zeros are interpreted in terms of the light quarks up and down.Comment: 34 pages, 14 figure

Bidirectional quantum teleportation of even and odd coherent states through the multipartite Glauber coherent state: Theory and implementation

Quantum teleportation has become a fundamental building block of quantum technologies, playing a vital role in the development of quantum communication networks. Here, we present a bidirectional quantum teleportation (BQT) protocol that enables even and odd coherent states to be transmitted and reconstructed over arbitrary distances in two directions. To this end, we employ the multipartite Glauber coherent state, comprising the Greenberger-Horne-Zeilinger, ground and Werner states, as a quantum resource linking distant partners Alice and Bob. The pairwise entanglement existing in symmetric and antisymmetric multipartite coherent states is explored, and by controlling the overlap and number of probes constructing various types of quantum channels, the teleportation efficiency of teleported states in both directions may be maximized. Besides, Alice's and Bob's trigger phases are estimated to explore their roles in our protocol using two kinds of quantum statistical speed referred to as quantum Fisher information (QFI) and Hilbert-Schmidt speed (HSS). Specifically, we show that the lower bound of the statistical estimation error, quantified by QFI and HSS, corresponds to the highest fidelity from Alice to Bob and conversely from Bob to Alice, and that the choice of the pre-shared quantum channel has a critical role in achieving high BQT efficiency. Finally, we show how to implement the suggested scheme on current experimental tools, where Alice can transfer her even coherent state to Bob, and at the same time, Bob can transfer his odd coherent state to Alice

Superspin Chains Solutions from 4D Chern-Simons Theory

As a generalisation of the correspondence linking 2D integrable systems with 4D Chern-Simons (CS) gauge theory, superspin chains are realized by means of crossing electric and magnetic super line defects in the 4D CS with super gauge symmetry. The oscillator realization of Lax operators solving the RLL relations of integrability is obtained in the gauge theory by extending the notion of Levi decomposition to Lie superalgebras. Based on particular 3-gradings of Lie superalgebras, we obtain graded oscillator Lax matrices for superspin chains with internal symmetries given by $A(m-1\mid n-1)$, $B(m\mid n)$, $C(n)$ and $D(m\mid n)

Magnetic Skyrmions: Theory and Applications

Magnetic skyrmions have been subject of growing interest in recent years for their very promising applications in spintronics, quantum computation and future low power information technology devices. In this book chapter, we use the field theory method and coherent spin state ideas to investigate the properties of magnetic solitons in spacetime while focussing on 2D and 3D skyrmions. We also study the case of a rigid skyrmion dissolved in a magnetic background induced by the spin-tronics; and derive the effective rigid skyrmion equation of motion. We examine as well the interaction between electrons and skyrmions; and comment on the modified Landau-Lifshitz-Gilbert equation. Other issues, including emergent electrodynamics and hot applications for next-generation high-density efficient information encoding, are also discussed

Topological String on Toric CY3s in Large Complex Structure Limit

We develop a non planar topological vertex formalism and we use it to study the A-model partition function $\mathcal{Z}_{top}$ of topological string on the class of toric Calabi-Yau threefolds (CY3) in large complex structure limit. To that purpose, we first consider the $T^{2}\times R$ special Lagrangian fibration of generic CY3-folds and we give the realization of the class of large $\mu$ toric CY3-folds in terms of supersymmetric gauged linear sigma model with \emph{non zero} gauge invariant superpotentials $)$. Then, we focus on a one complex parameter supersymmetric $U(1)$ gauged model involving six chiral superfields ${\Phi_{i}}$ with $\mathcal{W}=\mu (\prod\nolimits_{i=0}^{5}\Phi_{i})$ and we use it to compute the function $\mathcal{Z}_{top}$ for the case of the local elliptic curve in the limit $\mu \to \infty$.Comment: Latex, 38 pages, 12 figures. To appear in Nucl Phys