We explore a link between AdS black hole thermodynamics and the deflection angle variation. Using the elliptic function analysis, we first study the phase structure of RN-AdS solutions in terms of optical aspects. Precisely, we find that the stable and the unstable phases can be derived from thermal variations of the deflection angle. Then, we investigate the Hawking-Page transition from the Gibbs energy optical dependence. Among others, we reveal that the large black hole/small black hole transition occurs at a specific value of the deflection angle. The finding results, being confirmed by the help of the Ruppeiner metric of the phase state space, indicate that the deflection angle can be exploited to unveil data on thermodynamics of AdS black holes.

We investigate the critical behaviors of four-dimensional Kerr-AdS black holes from quintessential Dark Energy (DE) contributions. Using a moduli space, coordinated by the DE state parameter [Formula: see text] and the quintessence field intensity [Formula: see text], we deal with three different [Formula: see text]-models. By elaborating analytical formulas of relevant thermodynamical quantities denoted by [Formula: see text], we find significant similarities and distinctions. Precisely, for the [Formula: see text]-model, we show that DE contributions stabilize such black holes. For the [Formula: see text]-model, however, we get a reversed DE effect. In the [Formula: see text]-model, Kerr-AdS black holes reveal a resistance regarding the usual DE effects. Exploiting the explicit formulas of such thermodynamical quantities, we give certain physical interpretations for thermal behaviors. Although such relevant distinctions, we show that the [Formula: see text]-models involve similar universal ratios associated with certain critical thermodynamical quantities. Then, we analyze the photon orbits in the presence of DE.

Using the toroidal compactification of string theory on [Formula: see text]-dimensional tori, [Formula: see text], we investigate dyonic objects in arbitrary dimensions. First, we present a class of dyonic black solutions formed by two different D-branes using a correspondence between toroidal cycles and objects possessing both magnetic and electric charges, belonging to [Formula: see text] dyonic gauge symmetry. This symmetry could be associated with electrically charged magnetic monopole solutions in stringy model buildings of the standard model (SM) extensions. Then, we consider in some detail such black hole classes obtained from even-dimensional toroidal compactifications, and we find that they are linked to [Formula: see text] Clifford algebras using the vee product. It is believed that this analysis could be extended to dyonic objects which can be obtained from local Calabi–Yau manifold compactifications.

Combining colored toric geometry and Lie symmetries, we engineer qubit systems in the context of the D-brane physics in type II superstrings. Concretely, we establish a correspondence between such quantum systems and a class of K3 isolated singularities using operation techniques of graph theory. We first analyze 1 andf 2-qubits in some details and show that they are associated with the geometric engineering of six dimensional gauge theories obtained from type IIA superstring in 104 A. Belhaj et al. the presence of D2-branes probing one and two su(2) singularities of the K3 surface, respectively. Using a possible factorization of vector fields, we reveal that the corresponding gauge symmetry breaking provides states of such qubit systems. After that, we discuss the corresponding entanglement. Applying graph theory operations to colored toric polyvalent geometry, we then investigate multi-qubits in terms of D2-branes probing several su(2) isolated singularities of the K3 surface. The gauge field factorization generates abelian toric manifolds interpreted as Cartan sub-symmetries. Subject Classifications: 32C35, 58A14, 81T30, 81P45, 83C57 Keyswords: String theory; Quantum information theory; Graph theory; Toric geometry; Mirror symmetry, Calabi-Yau singularities; Lie symmetries

Using dyonic solutions in the type IIA superstring theory on Calabi–Yau (CY) manifolds, we reconsider the study of black objects and quantum information theory using string/string duality in six dimensions. Concretely, we relate four-qubits with a stringy quaternionic moduli space of type IIA compactification associated with a dyonic black solution formed by black holes (BHs) and black 2-branes (B2B) carrying eight electric charges and eight magnetic charges. This connection is made by associating the cohomology classes of the heterotic superstring on [Formula: see text] to four-qubit states. These states are interpreted in terms of such dyonic charges resulting from the quaternionic symmetric space [Formula: see text] corresponding to a [Formula: see text] sigma model superpotential in two dimensions. The superpotential is considered as a functional depending on four quaternionic fields mapped to a class of Clifford algebras denoted as [Formula: see text]. A link between such an algebra and the cohomology classes of [Formula: see text] in heterotic superstring theory is also given.

Using Hodge diagram combinatorial data, we study qubit and fermionic Fock spaces from the point of view of type II superstring black holes based on complex compactifications. Concretely, we establish a one-to-one correspondence between qubits, fermionic spaces and extremal black holes in maximally supersymmetric supergravity obtained from type II superstring on complex toroidal and Calabi-Yau compactifications. We interpret the differential forms of the n-dimensional complex toroidal compactification as states of n-qubits encoding information on extremal black hole charges. We show that there are 2(n) copies of n qubit systems which can be split as 2(n) = 2(n-1)+2(n-1). More precisely, 2(n-1) copies are associated with even D-brane charges in type IIA superstring and the other 2(n-1) ones correspond to odd D-brane charges in IIB superstring. This correspondence is generalized to a class of Calabi-Yau manifolds. In connection with black hole charges in type IIA superstring, an n-qubit system has been obtained from a canonical line bundle of n factors of one-dimensional projective space CP1.

We develop a new geometric approach to deal with qubit information systems using colored graph theory.More precisely, we present a one to one correspondence between graph theory, and qubit systems, which may be explored to attack qubit information problems using toric 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 CP~1, CP~1× CP~1 and CP~1× CP~1× CP~1 toric varieties respectively. Using a geometric procedure referred to as a colored toric geometry, we show that the qubit physics can be converted into a scenario handling toric data of such manifolds by help of hypercube graph theory. Operations on toric information can produce universal quantum gates.

We investigate the heat properties of AdS Black Holes in higher dimensions. We consider the study of the corresponding thermodynamical properties including the heat capacity explored in the determination of the black hole stability. In particular, we compute the heat latent. To overcome the instability problem, the Maxwell construction, in the (T, S)-plane, is elaborated. This method is used to modify the the Hawking-Page phase structure by removing the negative heat capacity regions. Then, we discuss the thermodynamic cycle and the heat engines using the way based on the extraction of the work from a black hole solution.

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 CP^1, CP^1×CP^1 and CP^1×CP^1×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.

Inspired from the inflation brane world cosmology, we study the thermodynamics of a black hole solution in two dimensional dilaton gravity with an arctangent potential background. We first derive the two dimensional black hole geometry, then we examine its asymptotic behaviors. More precisely, we find that such behaviors exhibit properties appearing in some known cases including the Anti de Sitter and the Schwarzchild black holes. Using the complex path method, we compute the Hawking radiation. The entropy function can be related to the value of the potential at the horizon.

We discuss the mass gap in quantum Hall solitons embedded in superstring theory. In particular, we give two holographic models which are obtained from D-brane configurations in type IIB superstring compactifications. The first one deals with the monolayered system in the D3/D7 brane set up. The second model corresponds to a multilayered system which is described by intersecting D5-branes wrapping a particular set of 3-cycles. In both models, we have shown that the mass gap is related to the filling factor.

Using quiver gauge theories in (1+2)-dimensions, we give brane realizations of a class of Quantum Hall Solitons (QHS) embedded in Type IIA superstring on the ALE spaces with exotic singularities. These systems are obtained by considering two sets of wrapped D4-branes on 2-spheres. The space-time on which the QHS live is identified with the world-volume of D4-branes wrapped on a collection of intersecting 2-spheres arranged as extended Dynkin diagrams of Lie algebras. The magnetic source is given by an extra orthogonal D4-brane wrapping a generic 2-cycle in the ALE spaces. It is shown as well that data on the representations of Lie algebras fix the filling factor of the QHS. In case of finite Dynkin diagrams, we recover results on QHS with integer and fractional filling factors known in the literature. In case of hyperbolic bilayer models, we obtain amongst others values of filling factors appearing in graphene literature.

We engineer U(1)n Chern–Simons type theories describing fractional quantum Hall solitons (QHS) in 1 + 2 dimensions from M-theory compactified on eight-dimensional hyper-Kähler manifolds as target space of N = 4 sigma model. Based on M-theory/type IIA duality, the systems can be modeled by considering D6-branes wrapping intersecting Hirzebruch surfaces F0's arranged as ADE Dynkin Diagrams and interacting with higher-dimensional R-R gauge fields. In the case of finite Dynkin quivers, we recover well known values of the filling factor observed experimentally including Laughlin, Haldane and Jain series.

We construct the 11D supermembrane with topological central charges induced through an irreducible winding on a G2 manifold realized from the T7/Z2xZ2xZ2 orbifold construction. The hamiltonian H of the theory on a T7 target has a discrete spectrum. Within the discrete symmetries of H associated to large diffeomorphisms, the Z2xZ2xZ2 group of automorphisms of the quaternionic subspaces preserving the octonionic structure is relevant. By performing the corresponding identification on the target space, the supermembrane may be formulated on a G2 manifold, preserving the discretness of its supersymmetric spectrum. The corresponding 4D low energy effective field theory has N=1 supersymmetry.

Using a quaternionic formulation of the moduli space M (IIA/K3) of 10D type IIA superstring on a generic K3 complex surface with volume V0, 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 Zm central charges isotriplet of the 6D N=2 superalgebra. We construct explicitly the special hyper-Kähler geometry of M (IIA/K3) and show that the SO(4)×SO(20) invariant hyper-Kähler potential is given by H=H0+Tr[ln(1−V0−1S)] with Kähler leading term H0=Tr[lnV0] plus an extra term which can be expanded as a power series in V0−1 and the traceless and symmetric 3×3 matrix S. We also derive the holomorphic matrix prepotential G and the flux potential GBH of the 6D black objects induced by the topology of the RR field strengths F2=dA1 and F4=dA3 on the K3 surface and show that GBH reads as Q0+∑m=13qmZm. Moreover, we reveal that Zm=∑I=120QI(∫C2IJm) where the isotriplet Jm is the hyper-Kähler 2-form on the K3 surface. It is found as well that the uplifting to seven dimensions is quite similar to 4D/5D correspondence for back hole potential considered in arXiv: 0707.0964 [hep-ph]. Then we study the N=2 black object attractors in 6D and 7D obtained respectively from type IIA string and M-theory on K3.

Under the assumption on the fundamental character of the Holographic Principle as a primary principle guiding the behavior of our universe the saturation of the holographic limit is reasonable. On the other hand the Fischler-Susskind holographic prescription seems to be incompatible with closed cosmological models due to the apparently unavoidable recontraction of the particle horizon area. However we will show that the saturation of the Fischler-Susskind holographic prescription over a closed (although almost flat) cosmological model enforces a cosmological evolution very similar to the observed universe.

We analyze the validity of the generalized covariant entropy bound near the apparent horizon of isotropic expanding cosmological models. We encounter violations of the bound for cosmic times smaller than a threshold. By introducing an infrared cutoff we are able to mantain the bound for a radiation dominated universe. We study different physical mechanisms to restore the bound, as a non-additivity of the entropy at a fundamental level and/or a cosmological uncertainty relation.

A huge family of solvable potentials can be generated by systematically exploiting the factorization (Darboux) method. Starting from the free case, a large class of the known solvable families is thus reproduced, together with new ones. We explicitly find and solve several new singular potentials obtained by iteration from the V = 0 case; some of them have an E = 0 bound state and constant phase shift without being explicitly scale invariant. The new potentials are rational functions, and can be related to rational solutions of the KdV family.

The Thomas-Fermi equation for the electronic structure of the planar uniform-background model is solved with use of relativistic kinematics.Received 7 December 1987DOI:https://doi.org/10.1103/PhysRevA.38.1069©1988 American Physical Society

The modified Thomas-Fermi equation of a degenerate self-gravitating fermion gas in the presence of a non-vanishing cosmological constant is studied. A restrictive relation between the mass of the bound cluster and the value of the cosmological constant is obtained for a given fermion mass.