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Title:
Théorie-M sur des Variétes d'holonomie
G2
Author:
Lalla Btissam Drissi
Comments:
19 pages, no figures
Abstract:
L'un
des objectifs de ce papier consiste à ramener
la théorie-M, considérée comme
la limite des cinq différentes théories
des supercordes, à une théorie \`{a}
$3+1$ dimensions et avec un nombre de supercharges
minimal. Nous montrons que ce modèle ne se
ré}alise qu'à travers l'introduction
d'une variété très spéciale
d'holonomie $\mathbf{G}_{2}$. Par la suite, nous procédons
à l' étude des modèles résultants
de la compactification de la th\'{e} orie-M sur cette
variété dans ses deux cas: régulier
et singulier.
Title:
Magnetic Laplacians on differential forms of the
hyperbolic disc and Landau Levels
Authors:
Allal Ghanmi and Ahmed Intissar
Comments:
9
pages, no figures
Abstract:
The aim of this paper is to introduce the ``Magnetic
Laplacian" $\Box^p_{\nu,\rho}$; $\nu >0$
acting on differential $p$-forms, $p=0,1,2$, of
the hyperbolic disc $D_\rho$ of radius $\rho>0$
and to give the asymptotic behaviour of its point
spectrum when $\rho \longmapsto +\infty$. For $p=0$
we show that it leads to the Landau Levels of the
free Hamiltonian of a spinless electron moving on
the plane under the action of a uniform magnetic
field. For $p=1$, we recover the point spectrum
of the so-called Pauli-Schr\"odinger operators
for a particle $\frac 12$-spin moving in the plane
under a constant magnetic field of magnitude $4\nu$
Title:
Non
Simply Laced Quiver gauge Theories in Superstrings
Compactifications
Authors:
Adil Belhaj, El Hassan Saidi
Comments:
22 pages, 6 figures
Abstract:
We
study the geometric engineering of non simply laced
quiver gauge Theories, obtained from type II superstrings
and F-theory compactified on local elliptic Calabi-Yau
manifolds. We review the main lines of the toric geometry
for ALE spaces with ADE singularities which we extend
to non simply laced ordinary and affine singularities.
Then, we develop two classes of solutions depending
on the two possible realisations of the outer-automorphism
group of $\Delta$(ADE) toric graphs. In F-theory on
elliptic Calabi-Yau manifolds, we give explicit results
for the affine non simply laced toric data and the
corresponding BCFG mirror geometries. The latters
extend known results obtained in literature for the
affine ADE cases. We also study the geometric engineering
of $ N=1$ supersymmetric gauge theory in eight dimensions.
In type II superstrings compactified on local Calabi-Yau
threefolds, we complete the analysis for ordinary
ADE singularities by giving the explicit derivation
of non simply ones. Finally we develop the basis of
polyvalent toric geometry. The latter extends bivalent
and trivalent geometries, considered in the geometric
engineering method, and use it to derive a new solution
for the affine $\hat D_4$ singularity. Other features
are also discussed.
Title:
Superstring Theory on AdS Spaces in The Penrose Limit
Authors:
El Mostapha Sahraoui
Comments:
7 pages, no figures
Abstract:
We give a brief review on AdS/CFT correspondence,
then we discuss how string spectrum in flat space
and plane waves arises from the large $N$ limit of
$U(N)$ ${\cal N}=4$ super Yang Mills. We also explain
the operator-state correspondence for ths case of
${AdS_{5}}\times{ S^5}$ and ${AdS_{5}\times S^5}/{{\bf
Z}_{k}}$ in some details.
Title:
On Manifolds of $G_2$ Holonomy in M- theory compactifications
Authors:
Adil Belhaj
Comments:
8 pages, no figures
Abstract:
In this work, we present quotients $X_7={X_8\over
U(1)}$ of $G_2$ holonomy form toric" hyper-Kahler
eight real dimensional manifolds $X_8$ using $N=4$
sigma model, with $U(1)^r$ gauge symmetry, with ADE
Cartan vector charges. In particular, for the $ A_r$
Cartan matrix, the quotient space is a cone on a $
{S^2}$ bundle over $r$ intersecting $\bf WCP^2_{(1,2,1)}$
weighted projective spaces according to the $A_r$
Dynkin diagram.
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Title:
Fractional Quantum Hall Excitations as RdTS Highest
Weight State Representations
Authors:
I. Benkaddour, A. ELRhalami,
E. H Saidi
Comments:
22 pages, no figures
Abstract:
Using
the Chern-Simons effective model of fractional quantum
Hall (FQH) systems, we complete partial results obtained
in the literature on FQHE concerning topological orders
of FQH states. We show that there exists a class of
effective FQH models having the same filling fraction
$\nu$, interchanged under $ Gl(n,Z)$ transformations
and extends results on Haldane hierarchy. We also
show that Haldane states at any generic hierarhical
level n may be realised in terms of n Laughlin states
composites and rederive results for the n=2,3 levels
respectively associated with $\nu= {{2}\over{5}}$
and $\nu= {{3}\over{7}}$ filling fractions. We study
symmetries of the filling fractions series $\nu= {{p_2}\over{p_1
p_2 -1}}$ and $\nu= {{p_1 p_2 -1}\over{p_1 p_2 p_3
p_1 -p_2}}$, with $p_1$ odd and $p_2$ and $p_3$ even
integers, and show that, upon imposing the Gl(n,Z)
invariance, we get remarkable informations on their
stability. Then, we reconsider the Rausch de Traubenberg
and Slupinsky (RdTS) algebra recently obtained in
[1,2] and analyse its limit on the boundary $\partial({AdS_3})$
of the (1+2) dimensional manifold $AdS_3$. We show
that generally one may distinguish bulk highest weight
states (BHWS) living in $AdS_3$ and edge highest weight
states (EHWS)living on the border $\partial({AdS_3})$.
We explore these two kinds of RdTS representations
carrying fractional values of the spin and propose
them as condidates to describe the FQH states.
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Title:
Type IIB String Backgrounds on Parallelizable PP-Waves
and Conformal Liouville Theory
Authors:
Mounia Hssaini, Moulay Brahim
Sedra
Comments:
9 pages, no figures
Abstract:
The scope of this work concerns the adaptation of
the parallelizability pp-wave (Ppp-wave) process to
$D=10$ type IIB string backgrounds in the presence
of the non-trivial anti-self dual R-R 5-form ${\cal
F}$. This is important in the sense that it gives
rise to some unsuspected properties. In fact, exact
solutions of type IIB string backgrounds on Ppp-waves
are discussed. For the $u$-dependence of the dilaton
field $\Phi $, we establish explicitly a correspondence
between type IIB supergravity equations of motion
and $2d$-conformal Liouville field theory. We show
also that the corresponding conserved conformal current
$T(\Phi)$ coincides exactly with the trace of the
symmetric matrix $\mu _{ij}$ appearing in the quadratic
front factor $F = \mu_{ij}x^{i} x^{j}$ of the Ppp-wave.
Furthermore, we consider the transverse space dependence
of the dilaton $\Phi$ and show that the supergravity
equations are easily solved for the linear realization
of the dilaton field. Other remarkable properties
related to this case are also discussed.
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Title:
Supersymmetric contributions to the CP asymmetry of
the $B\to\phiK_S$ and $B\to\eta'K_S$
Authors: Shaaban Khalil
Comments: 7 pages, 10 figures
Abstract:
We analyse the CP asymmetry of the $B \to \phi K_S$
and $B\to \eta' K_S$ processes in general supersymmetric
models. We consider both gluino and chargino exchanges
in a model independent way by using the mass insertion
approximation method. We adopt the QCD factorization
method for evaluating the corresponding hadronic matrix
elements. We show that chromomagnetic type of operator
may play an important role in accounting for the deviation
of the mixing CP asymmetry between $B \to \phi K_S$
and $B \to J/\psi K_S$ processes observed by Belle
and BaBar experiments. We also show that due to the
different parity in the final states of these processes,
their supersymmetric contributions from the R-sector
have an opposite sign, which naturally explain the
large deviation between their asymmetries.
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Title:
Two – Dimensional Quantum(4,4) Null Superstring
in de Sitter Space
Authors: F. Assaoui and T. Lhallabi
Comments: 16 pages, no figures
Abstract:
The (4,4) null superstring
equations of motions and constraints on de Sitter
space are given by using the harmonic superspace.
These are solved explicitly by performing a perturbative
expansion of the (4,4) superstring coordinates in
powers of , the world-sheet speed of light. The analytic
expressions of the zeroth and first order solutions
are determined. On the other hand, we study the quantization
of the (4,4) null superstring in de Sitter space and
we describe its superalgebra.
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© African Journal of Mathematical Physics |
