Algebraic geometry realization of quantum Hall soliton

Abounasr, R.; Haddou, Malika Ait Ben; Rhalami, A. El; Saidi, El Hassan

doi:10.1063/1.1834695

Cited by 7 publications

(2 citation statements)

References 28 publications

(26 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(v) The p-branes of type IIA and type IIB string theory in 10 dimensions correspond to classes of rational curves on B 1 and CP 1 × CP 1 , respectively. Further explicit realization of these is given in [AHRS05].…”

Section: Introductionmentioning

confidence: 99%

Mysterious Triality and Rational Homotopy Theory

Sati¹,

Voronov²

2021

Preprint

View full text Add to dashboard Cite

Mysterious duality has been discovered by Iqbal, Neitzke, and Vafa [INV02] as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series E k .It turns out that the sequence of del Pezzo surfaces is not the only sequence of objects in mathematics which gives rise to the same E k symmetry pattern. We present a sequence of topological spaces, starting with the four-sphere S 4 , and then forming its iterated cyclic loop spaces L k c S 4 , within which we discover the E k symmetry pattern via rational homotopy theory. For this sequence of spaces, the correspondence between its E k symmetry pattern and that of toroidal compactifications of M-theory is no longer a mystery, as each space L k c S 4 is naturally related to the compactification of M-theory on the k-torus via identification of the equations of motion of (11 − k)-dimensional supergravity as the defining equations of the Sullivan minimal model of L k c S 4 . This gives an explicit duality between algebraic topology and physics.Thereby, we extend Iqbal-Neitzke-Vafa's mysterious duality between algebraic geometry and physics into a triality, also involving algebraic topology. Via this triality, duality between physics and mathematics is demystified, and the mystery is transferred to the mathematical realm as duality between algebraic geometry and algebraic topology. Now the question is: is there an explicit relation between the del Pezzo surfaces B k and iterated cyclic loop spaces of S 4 which would explain the common E k symmetry pattern?

show abstract

Section: Introductionmentioning

confidence: 99%

Mysterious Triality and Rational Homotopy Theory

Sati¹,

Voronov²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The system has been placed in a background of coincident D6-branes extended in the directions perpendicular to the world-volume of the D2-brane on which QHE resides. Some further details on this construction can be found in [3]- [10]. However, this type IIA superstring construction has been done in ten dimensional space-time.…”

Section: Introductionmentioning

confidence: 99%

Engineering of Quantum Hall Effect from type IIA string theory on the K3 surface

Belhaj

Seguí

2010

Physics Letters B

View full text Add to dashboard Cite

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.

show abstract