On Geometric Engineering of Supersymmetric Gauge Theories

We present the basic ideas of geometric engineering of the supersymmetric quantum field theories viewed as a low energy limit of type II strings and F-theory on singular Calabi Yau manifolds. We first give the main lines of toric geometry as it is a powerful technique to deal compact complex manifolds. Then we introduce mirror symmetry which plays a crucial role in the study of superstring dualities and finally we give elements on Calabi Yau singularities. After that we study the geometric engineering of N=2 supersymmetric gauge theories in six and four dimensions. Finally we make comments regarding $N=1$ SYM in four dimensions.Comment: 8 pages. To be published in the proceedings of the Workshop on Noncommutative Geometry, Superstrings and Particle Physics. Rabat -Morocco, (16-17 June 2000

On Geometric Engineering of N=1 ADE Quiver Models

In this talk, we discuss four-dimensional N=1 affine $ADE$ quiver gauge models using the geometric engineering method in M-theory on $G_2$ manifolds with K3 fibrations.Comment: 10 pages, LaTex, Contribution to the Proceedings of the Workshop on Quantum Field Theory, Geometry and Non Perturbative Physics, Rabat, July 28th-29th, 200

On Black Objects in Type IIA Superstring Theory on Calabi-Yau Manifolds

The compactification of type IIA superstring on n-dimensional Calabi-Yau manifolds is discussed. In particular, a conjecture is given for type IIA extremal p-dimensional black brane attractors corresponding to Ads_{p+2}\times S^{8-2n-p} horizon geometries.Comment: 9 pages, Latex. Minor changes. Version to be publishe

On Geometric Transitions in String Compactifications

We reconsider the study of the geometric transitions and brane/flux dualities in various dimensions. We first give toric interpretations of the topology changing transitions in the Calabi-Yau conifold and the $Spin(7)$ manifold. The latter, for instance, can be viewed as three intersecting Calabi-Yau conifolds according to \cp^2 toric graph. Orbifolds of such geometries are given in terms of del Pezzo complex surfaces. Second we propose a four-dimensional F-theory interpretation of type IIB geometric transitions on the Calabi-Yau conifold. This gives a dual description of the M-theory flop in terms of toric mirror symmetry. In two dimensions, we study the geometric transition in a singular $Spin(7)$ manifold constructed as a cone on SU(3)/U(1). In particular, we discuss brane/flux duality in such a compactification in both type IIA and type IIB superstrings. These examples preserve one supercharge and so have ${\cal N}= 1/2$ supersymmetry in two dimensions. Then, an interpretation in terms of F-theory is given.Comment: 21 pages, latex. Based on invited talks presented at the IX-th Workshop on Mathematical Physics and Applications, Rabat, 23-25 February 2004 and the Workshop of Geometry and Physics of Particles, Fields, and Strings, Zaragoza, 24-28 May 2004. Minor changes. Note added, with comments and additional reference

Manifolds of G_2 Holonomy from N=4 Sigma Model

Using two dimensional (2D) N=4 sigma model, with $U(1)^r$ gauge symmetry, and introducing the ADE Cartan matrices as gauge matrix charges, we build " toric" hyper-Kahler eight real dimensional manifolds X_8. Dividing by one toric geometry circle action of X_8 manifolds, we present examples describing quotients $X_7={X_8\over U(1)}$ of G_2 holonomy. In particular, for the A_r Cartan matrix, the quotient space is a cone on a ${S^2}$ bundle over r intersecting $\bf WCP^2_{(1,2,1)}$ projective spaces according to the A_r Dynkin diagram.Comment: Latex, 14 pages. Some comments are added,typos fixed. One reference added [17]. Final version accepted for publication in the J. Phys.A: Math.Gen.35(2002

Quantum Information and Elementary Particles

Motivated by string theory and standard model physics, we discuss the possibility of other particles-based quantum information. A special attention is put on the consideration of the graviton in light of the gravitational wave detection. This may offer a new take in approaching quantum information using messenger particles. The construction is readily extended to higher dimensional qubits where we speculate on possible connections with open and closed string sectors in terms of quiver and graph theories, respectively. In particular, we reveal that the vectorial qubits could be associated with skeleton diagrams considered as extended quivers.Comment: 10 pages, latex fil

F-theory and N=1 Quivers from Polyvalent Geometry

We study four dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K\"{a}hler structure. Using intersecting complex toric surfaces, we derive a class of N=1 quivers with charged fundamental matter placed on external nodes. The emphasis is on how local Calabi-Yau equations solve the corresponding physical constraints including the anomaly cancelation condition. Concretely, a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.Comment: Latex, 16 pages, 4 figures. Minor modifications. Accepted version in Communications in Theoretical Physics (CPT

QFT method for indefinite Kac-Moody Theory: A step towards classification

We propose a quantum field theory (QFT) method to approach the classification of indefinite sector of Kac-Moody algebras. In this approach, Vinberg relations are interpreted as the discrete version of the QFT_{2} equation of motion of a scalar field and Dynkin diagrams as QFT_{2} Feynman graphs. In particular, we show that Dynkin diagrams of su(n+1) series (n\geq 1) can be interpreted as free field propagators and T_{p,q,r} diagrams as the vertex of \phi^{3} interaction. Other results are also given.Comment: 13 pages, 3 figure

On 750 GeV Diphoton Resonance in Stringy Standard-Like Models

The LHC diphoton excess 750 GeV is discussed in a string-inspired standard-like model. Precisely, a singlet scalar-extended SM from a vacua of four stacks of intersecting D6-branes giving rise to a large gauge symmetry is considered. Besides its relevant couplings to the SM sector, the involved scales allow for a scalar mass near to the reported diphoton excess.Comment: 9 pages, 2 figures, 3 tables. Minor changes and references adde

Lie symmetries and 2D Material Physics

Inspired from Lie symmetry classification, we establish a correspondence between rank two Lie symmetries and 2D material physics. The material unit cell is accordingly interpreted as the geometry of a root system. The hexagonal cells, appearing in graphene like models, are analyzed in some details and are found to be associated with A_2 and G_2 Lie symmetries. This approach can be applied to Lie supersymmetries associated with fermionic degrees of freedom. It has been suggested that these extended symmetries can offer a new way to deal with doping material geometries. Motivated by Lie symmetry applications in high energy physics, we speculate on a possible connection with (p,q) brane networks used in the string theory compactification on singular Calabi-Yau manifolds.Comment: 15 pages, Late