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We study the geometric engineering of supersymmetric quantum field theories (QFT), with non simply laced gauge groups, obtained from superstring and F-theory compactifications on local Calabi-Yau manifolds. First we review the main lines... more
We study the geometric engineering of supersymmetric quantum field theories (QFT), with non simply laced gauge groups, obtained from superstring and F-theory compactifications on local Calabi-Yau manifolds. First we review the main lines of the toric method for ALE spaces with ADE singularities which we extend to non simply laced ordinary and affine singularities. Then, we develop two classes of
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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... more
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
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We develop the non-commutative harmonic space (NHS) analysis to study the problem of solving the nonlinear constraint equations of non-commutative Yang-Mills self-duality in four dimensions. We show that this space, denoted also as... more
We develop the non-commutative harmonic space (NHS) analysis to study the problem of solving the nonlinear constraint equations of non-commutative Yang-Mills self-duality in four dimensions. We show that this space, denoted also as NHS(eta,theta), has two SU(2) isovector deformations eta(ij) and theta(ij) parametrizing, respectively, two non-commutative harmonic subspaces NHS(eta,0) and NHS(0, theta) used to study the self-dual and anti self-dual
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We discuss quiver gauge models with bi-fundamental and fundamental matter obtained from F-theory compactified on ALE spaces over a four dimensional base space. We focus on the base geometry which consists of intersecting F0=CP1xCP1... more
We discuss quiver gauge models with bi-fundamental and fundamental matter obtained from F-theory compactified on ALE spaces over a four dimensional base space. We focus on the base geometry which consists of intersecting F0=CP1xCP1 Hirzebruch complex surfaces arranged as Dynkin graphs classified by three kinds of Kac-Moody (KM) algebras: ordinary, i.e finite dimensional, affine and indefinite, in particular hyperbolic. We interpret the equations defining these three classes of generalized Lie algebras as the anomaly cancelation condition of the corresponding N =1 F-theory quivers in four dimensions. We analyze in some detail hyperbolic geometries obtained from the affine A base geometry by adding a node, and we find that it can be used to incorporate fundamental fields to a product of SU-type gauge groups and fields.
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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,... more
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.
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... more
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.
Using toric Cartan matrices as abelian gauge charges, we present a class of stringy fractional quantum Hall effect (FQHE) producing some recent experimental observed filling factor values. More precisely, we derive the corresponding... more
Using toric Cartan matrices as abelian gauge charges, we present a class of stringy fractional quantum Hall effect (FQHE) producing some recent experimental observed filling factor values. More precisely, we derive the corresponding Chern-Simons type models from M-theory compactified on four complex dimensional hyper-K\"{a}hler manifolds X^4. These manifolds, which are viewed as target spaces of a particular N=4 sigma model in two dimensions, are identified with the cotangent bundles over intersecting 2-dimensional toric varieties V_i^2 according to toric Cartan matrices. Exploring results of string dualities, the presented FQHE can be obtained from D6-banes wrapping on such intersecting toric varieties interacting with R-R gauge fields. This string theory realization provides a geometric interpretation of the filling factors in terms of toric and Euler characteristic topological data of the compactified geometry. Concretely, explicit bilayer models are worked out in some details.
We develop a new approach to deal with qubit information systems using toric geometry and its relation to Adinkra graph theory. More precisely, we link three different subjects namely toric geometry, Adinkras and quantum information... more
We develop a new approach to deal with qubit information systems using toric geometry and its relation to Adinkra graph theory. More precisely, we link three different subjects namely toric geometry, Adinkras and quantum information theory. This one to one correspondence may be explored to attack qubit system problems using geometry considered as a powerful tool to understand modern physics including string theory. Concretely, we examine in some details the cases of one, two, and three qubits, and we find that they are associated with \bf CP^1, \bf CP^1\times CP^1 and \bf CP^1\times CP^1\times CP^1 toric varieties respectively. Using a geometric procedure referred to as colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of Adinkra graph theory. Operations on toric information can produce universal quantum gates.
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ABSTRACT In this paper, we investigate the Blume-Capel thin film model for mixed spins σ = 3/2 and S = 2 placed on a square lattice with four-spin interactions. In fact, we study the effect of the coupling exchange interactions in the... more
ABSTRACT In this paper, we investigate the Blume-Capel thin film model for mixed spins σ = 3/2 and S = 2 placed on a square lattice with four-spin interactions. In fact, we study the effect of the coupling exchange interactions in the presence of both an external and a crystal field. The ground state phase diagrams are studied for this mixed system, and the stable phases have been established. On the other hand, the magnetic properties, at non-null temperatures are investigated using the Monte Carlo simulations. In order to complete this study, we present the thermal behaviors of the hysteresis loops. The dependencies of the coercitif magnetic field on the crystal field, and/or the four-spin interaction couplings, are also discussed.
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ABSTRACT In this paper, we investigate the Blume-EmeryGriffiths thin film model, for mixed spins =3/2 and S=2, with a biquadratic exchange interaction. More precisely, we study the effect of the coupling exchange interactions in the... more
ABSTRACT In this paper, we investigate the Blume-EmeryGriffiths thin film model, for mixed spins =3/2 and S=2, with a biquadratic exchange interaction. More precisely, we study the effect of the coupling exchange interactions in the presence of both an external magnetic and crystal fields. We first elaborate analytically the ground state phase diagrams. Concretely, the stable phases have been discussed. Then, the magnetic properties, at non vanishing temperature, are illustrated using Monte Carlo calculations. To complete this study, we examine the hysteresis loops behavior of the system.
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ABSTRACT Using Monte Carlo method, we study the magnetic proprieties of La2FeCoO6 double perovskite. First, we elaborate the ground state phase diagrams in different planes: (R1,R2), (R1,d), (R2,d), (R1,h), (R2,h) and (h, d), where, the... more
ABSTRACT Using Monte Carlo method, we study the magnetic proprieties of La2FeCoO6 double perovskite. First, we elaborate the ground state phase diagrams in different planes: (R1,R2), (R1,d), (R2,d), (R1,h), (R2,h) and (h, d), where, the reduced parameters R1=JFe-Fe/JFe-Co, R2=JCo-Co/JFe-Co, d=Δ/JFe-Co and h=H/JFe-Co represent the reduced Fe-Fe, Co-Co exchange coupling interactions, the reduced crystal field and the reduced external magnetic field, respectively. We show that the only stable configurations in these planes are: (±2, ±1/2), (±1, ±1/2) and (0, ±1/2). Then, we investigate the thermal behavior of the magnetizations and the susceptibilities of such a system for the ferromagnetic case. Moreover, we reveal that the increasing exchange Fe-Fe coupling effect increases the critical temperature. We also discuss the hysteresis cycle loops.
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We investigate the statistical behaviors of 3D hairy black holes in the presence of a scalar field. The present study is made in terms of two relevant parameters: rotation parameter a and B parameter related to the scalar field. More... more
We investigate the statistical behaviors of 3D hairy black holes in the presence of a scalar field. The present study is made in terms of two relevant parameters: rotation parameter a and B parameter related to the scalar field. More precisely, we compute various statistical quantities including the partition function for non-charged and charged black hole solutions. Using a partition function calculation, we show that the probability is independent of a and B parameters.
We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex cycles with genus $g$. Using toric... more
We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex cycles with genus $g$. Using toric geometry, A(1,0) quivers are analyzed in some details and it is shown that A(1,0) can be used to incorporate fundamental fields to a product of two unitary factor groups. We expect that this approach can be applied to other kinds of Lie superalgebras;
Interpreting the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the investigation of P-V critical behaviors of (1+n)-dimensional topological AdS black holes in... more
Interpreting the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the investigation of P-V critical behaviors of (1+n)-dimensional topological AdS black holes in Lovelock-Born-Infeld gravity. In particular, we give an explicit expression of the universal number \chi=\frac{P_c v_c}{T_c} in terms of the space dimension $n$. Then, we examine the phase transitions at the critical points of such topological black holes for 6 \leq n \leq 11 as required by the physical condition of the thermodynamical quantities. More precisely, the Ehrenfest equations have been checked revealing that the black hole system undergoes a second phase transition at the critical points.
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ABSTRACT Inspired from the connection between Lie symmetries and two-dimensional materials, we propose a new statistical lattice model based on a double hexagonal structure appearing in the G2 symmetry. We first construct an Ising-1/2... more
ABSTRACT Inspired from the connection between Lie symmetries and two-dimensional materials, we propose a new statistical lattice model based on a double hexagonal structure appearing in the G2 symmetry. We first construct an Ising-1/2 model, with spin values σ = ±1, exhibiting such a symmetry. The corresponding ground state shows the ferromagnetic, the antiferromagnetic, the partial ferrimagnetic and the topological ferrimagnetic phases depending on the exchange couplings. Then, we examine the phase diagrams and the magnetization using the mean field approximation (MFA). Among others, it has been suggested that the present model could be localized between systems involving the triangular and the single hexagonal lattice geometries.
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Using Katz, Klemm and Vafa geometric engineering method of $\mathcal{N}=2$ supersymmetric QFT$_{4}$s and results on the classification of generalized Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of... more
Using Katz, Klemm and Vafa geometric engineering method of $\mathcal{N}=2$ supersymmetric QFT$_{4}$s and results on the classification of generalized Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of $\mathcal{N}=2$ CFT$_{4}$s based on \textit{indefinite} singularities. We show that the vanishing condition for the general expression of holomorphic beta function of $\mathcal{N}=2$ quiver gauge QFT$_{4}$s coincides exactly with the