Using M-theory compactification, we develop a three factor separation for the scalar submanifold of N=2 seven dimensional supergravity associated with 2-cycles of the K3 surface. Concretely, we give an interplay between the three scalar submanifold factors and the extremal black holes obtained from M2-branes wrapping such 2-cycles. Then, we show that the corresponding black hole charges are linked to one, two and four qubit systems.

Using graph theory based on Adinkras, we consider once again the study of extremal black branes in the framework of quantum information. More precisely, we propose a one to one correspondence between qubit systems, Adinkras and certain extremal black branes obtained from type IIA superstring compactified on T^n. We accordingly interpret the real Hodge diagram of T^n as the geometry of a class of Adinkras formed by 2^n bosonic nodes representing n qubits. In this graphic representation, each node encodes information on the qubit quantum states and the charges of the extremal black branes built on T^n. The correspondence is generalized to n superqubits associated with odd and even geometries on the real supermanifold T^n|n. Using a combinatorial computation, general expressions describing the number of the bosonic and the fermionic states are obtained.

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G 2, Spin(7), O(8) as well as E 8 and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.

We explore the four dimensional Einstein-Maxwell landscape as a toy model in which we can formulate a sphere compactification stabilized by an electromagnetic field. Replacing the compactification sphere by J spheres, we obtain a simple sector of the (2J+2)-dimensional Einstein-Maxwell landscape. In this toy model, we analyze some properties which are very difficult to uncover in the string theory landscape, including: complete moduli stabilization, stability conditions, and state counting. We also show how to construct anthropic states in this model. A detailed comparison between the main features of this landscape and the Bousso-Polchinski landscape is given. We finally speculate on the impact of these phenomena in the string theory landscape.

A toy landscape sector is introduced as a compactification of the Einstein-Maxwell model on a product of two spheres. Features of the model include moduli stabilization, a distribution of the effective cosmological constant of the dimensionally reduced 1 + 1 spacetime, which is different from the analogous distribution of the Bousso-Polchinski landscape, and the absence of the so-called α* problem. This problem arises when the Kachru-Kallosh-Linde-Trivedi stabilization mechanism is naively applied to the states of the Bousso-Polchinski landscape. The model also contains anthropic states, which can be readily constructed without needing any fine-tuning.

A brane picture in Type IIA superstring for the Yang Monopole is reconsidered. It makes use of D2 and D4-branes wrapped on cycles in the K3 surface. When the model was first presented some problems concerning the charges of the monopoles arised. In this paper, they are shown to be cured by the model itself. Surprisingly, the incompatibility between the multi-charge configuration and the spherical symmetry of the Yang Monopole is seen in the brane description as the emergence of the enhancon shell and the fuzzy geometry. This consistency is deep and surprising, and is the point that triggered this work. It nontrivially relates a purely geometrical problem in ordinary spacetime with the emergence of noncommutative geometries. Besides, this paper includes an extended model for SO(4)-monopoles, a T-dual model in Type IIB superstring and an analysis on the possible duality between our model and another setup in M-Theory/Heterotics for the Yang monopole found before.

We discuss a class of three-dimensional [Formula: see text] Chern–Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex four-dimensional hyper-Kähler (HK) manifolds, which are realized explicitly as a cotangent bundle over two-Fano toric varieties V2. The corresponding CS gauge models are encoded in quivers similar to toric diagrams of V2. Using toric geometry, it is shown that the constraints on CS levels can be related to toric equations determining V2.

The Bousso-Polchinski (BP) Landscape is a proposal for solving the Cosmological Constant Problem. The solution requires counting the states in a very thin shell in flux space. We find an exact formula for this counting problem which has two simple asymptotic regimes, one of them being the method of counting low Λ states given originally by Bousso and Polchinski. We finally give some applications of the extended formula: a robust property of the Landscape which can be identified with an effective occupation number, an estimator for the minimum cosmological constant and a possible influence on the KKLT stabilization mechanism.

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 F 0 = CP 1 × CP 1 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 [Formula: see text] 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.

Reconsidering the analysis of the moduli space of N = 2 eight-dimensional supergravity coupled to seven scalars, we propose a new scalar manifold factorization given by SO(2, 2)/(SO(2) × SO(2)) × SO(2, 1)/SO(2) × SO(1, 1). This factorization is supported by the appearance of three solutions of Type IIA extremal black p-branes (p = 0, 1, 2) with AdSp + 2 × S6 − p near-horizon geometries in eight dimensions. We analyze the corresponding attractor mechanism. In particular, we give an interplay between the scalar manifold factors and the extremal black p-brane charges. Then we show that the dilaton can be stabilized by the dyonic black 2-brane charges.

Using D-brane configurations on the K3 surface, we give six-dimensional type IIA stringy realizations of the Quantum Hall Effect (QHE) in 1+2 dimensions. Based on the vertical and horizontal lines of the K3 Hodge diamond, we engineer two different stringy realizations. The vertical line presents a realization in terms of D2 and D6-branes wrapping the K3 surface. The horizontal one is associated with hierarchical stringy descriptions obtained from a quiver gauge theory living on a stack of D4-branes wrapping intersecting 2-spheres embedded in the K3 surface with deformed singularities. These geometries are classified by three kinds of the Kac–Moody algebras: ordinary, i.e. finite dimensional, affine and indefinite. We find that no stringy QHE in 1+2 dimensions can occur in the quiver gauge theory living on intersecting 2-spheres arranged as affine Dynkin diagrams. Stringy realizations of QHE can be done only for the finite and indefinite geometries. In particular, the finite Lie algebras give models with fractional filling fractions, while the indefinite ones classify models with negative filling fractions which can be associated with the physics of holes in the graphene.

We study holonomy groups coming from F-theory compactifications. We focus mainly on SO(8) as 12−4=8 and subgroups SU(4), Spin(7), G 2 and SU(3) suitable for descent from F-theory, M-theory and Superstring theories. We consider the relation of these groups with the octonions, which is striking and reinforces their role in higher dimensions and dualities. These holonomy groups are related in various mathematical forms, which we exhibit.

The Bousso-Polchinski landscape is a proposal for solving the cosmological constant problem. The solution requires counting the states in a very thin shell in flux space. We find an exact formula for this counting problem which has two simple asymptotic regimes, one of them being the method of counting low Lambda states given originally by Bousso and Polchinski. We finally give some applications of the extended formula: a robust property of the landscape which can be identified with an effective occupation number, an estimator for the minimum cosmological constant, and a possible influence on the Kachru-Kallosh-Linde-Trivedi stabilization mechanism.