El Hassan Saidi

N = 2 Supersymmetric Black Attractors in Six and Seven Dimensions

Using a quaternionic formulation of the moduli space M (IIA/K3) of 10D type IIA superstring on a generic K3 complex surface with volume V 0, we study extremal N = 2 black attractors in 6D space-time and their uplifting to 7D. For the 6D theory, we exhibit the role played by 6D N = 1 hypermultiplets and the Z m central charges isotriplet of the 6D N = 2 superalgebra. We construct explicitly the special hyperKahler geometry of M (IIA/K3) and show that the SO(4)×SO(20)

Geometric engineering of CFT4 based on indefinite singularities: hyperbolic case

Abstract Using Katz, Klemm and Vafa geometric engineering method of N =2 supersymmetric QFT4 and results on the classification of generalized Cartan matrices of Kac–Moody (KM) algebras, we study the unexplored class of N =2 CFT4 based on indefinite singularities. We show that the vanishing condition for the general expression of holomorphic beta function of N =2 quiver gauge QFT4 coincides exactly with the fundamental classification theorem of KM algebras. Explicit solutions are derived for mirror geometries of CY threefolds with hyperbolic singularities.

Toric Calabi-Yau supermanifolds and mirror symmetry

We study mirror symmetry of supermanifolds constructed as fermionic extensions of compact toric varieties. We mainly discuss the case where the linear sigma A-model contains as many fermionic fields as there are U(1) factors in the gauge group. In the mirror super-Landau-Ginzburg B-model, focus is on the bosonic structure obtained after integrating out all the fermions. Our key observation is that there is a relation between the super-Calabi-Yau conditions of the A-model and quasi-homogeneity of the B-model, and that the degree of the associated superpotential in the B-model is given in terms of the determinant of the fermion charge matrix of the A-model.

Classification of N = 2 supersymmetric CFT 4 s: Indefinite Series

Using the geometric engineering method of 4D quiver gauge theories and results on the classification of Kac?Moody (KM) algebras, we show by explicit examples that there exist three sectors of infrared CFT4s. Since the geometric engineering of these CFT4s involves type II strings on K3 fibred CY3 singularities, we conjecture the existence of three kinds of singular complex surfaces containing, in addition to the two standard classes, a third indefinite set. To illustrate this hypothesis, we give explicit examples of K3 surfaces with H43 and E10 hyperbolic singularities. We also derive a hierarchy of indefinite complex algebraic geometries based on affine Ar and T(p,q,r) algebras going beyond the hyperbolic subset. Such hierarchical surfaces have a remarkable signature that is manifested by the presence of poles.

RG Cascades in Hyperbolic Quiver Gauge Theories

Abstract In this paper, we provide a general classification of supersymmatric QFT 4 s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super- QFT 4 s. This includes, amongst others, its embedding in type II string on local Calabi–Yau threefolds. We give realizations of these supersymmetric QFT 4 s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non-zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made.

Electronic properties and hidden symmetries of graphene

Using the relation between the structural and the electronic properties of honeycomb, we study the hidden SU (3) symmetry of the graphene monolayer and exhibit the link with its electronic properties. We show that the conservation law of incoming and outgoing electronic momenta at each site of graphene is solved in terms of SU(3) representations; and the Fourier waves ˜ �(kx,ky) of the hopping �

Four Dimensional Graphene

Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD given in [P. F. Bedaque et al. Phys. Rev. D78 (2008) 017502] by using the hidden SU (5) symmetry of the 4D hyperdiamond lattice H4. We first study the link between the H4 and SU (5); then we refine the BBTW 4D lattice action by using the weight vectors �1, �2, �3, �4, �5 of the 5-dimensional representation

Entropy of pairs of dual attractors in six and seven dimensions

We study the attractor mechanism of dual pairs of black brane bounds in = 2 supergravity in six and seven dimensions. First, we consider the effective potentials of the 6D and 7D black branes as well as their entropies. The contribution coming from the SO(1,1) factor of the moduli spaces M6D and M7D of these theories is carefully analyzed and it is used to motivate the study of the dual black branes bounds; which in turn allow to fix the critical value of the dilaton at horizon. The attractor eqs. of the black branes and the bound pairs are derived by combining the criticality conditions of the corresponding effective potentials and the Lagrange multiplier method capturing constraints eqs. on the fields moduli.

Solitons on compact and non-compact spaces in large non-commutativity

We study solitons at the minima of scalar field potentials for Moyal spaces and torii in large non-commutativity and interpret these solitons in terms of non-BPS D-branes of string theory. We derive a mass spectrum formula linking different D-branes together on quantum torii and suggest that it describes general systems of D-brane bound states, which extend the \mbox{{\rm D}2-{\rm D}0} one. Then we propose a shape for the effective potential approaching these quasi-stable bound states. We give the gauge symmetries of these systems of branes and show that they depend on the quantum torii representations.

NC Branes and Hierarchies in Quantum Hall Fluids

We develop the non-commutative Chern-Simons gauge model analysis modeling the description of the hierarchical states of fractional quantum Hall fluids. For a generic level n of the hierarchy, we show that the order parameter matrix Kab is given by θ−2Tr (τaτb), where {τa,1 ≤ a ≤ n} define a specific set of n × n matrices depending on the parameter θ and the levels la of the CS effective field theory. Our analysis predicts the existence of a third order tensor of order parameters Cabc induced by the external magnetic field. It is shown that the Cabcs are not new order parameters and are given by θdabc, where dabc are numbers depending on the las. We also give the generalized quantum Hall soliton extending that obtained in the case of the Laughlin state.