BRANE REALIZATIONS OF QUANTUM HALL SOLITONS AND LIE ALGEBRAS

2012 ◽  
Vol 09 (03) ◽  
pp. 1250017
Author(s):  
A. BELHAJ ◽  
A. ELRHALAMI ◽  
N.-E. FAHSSI ◽  
M. J. I. KHAN ◽  
E. H. SAIDI ◽  
...  
Keyword(s):  
Lie Algebras ◽  
Filling Factor ◽  
Gauge Theories ◽  
Quantum Hall ◽  
Space Time ◽  
Magnetic Source ◽  
Dynkin Diagrams ◽  
World Volume ◽  
The World ◽  
Representations Of Lie Algebras

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.

scholarly journals Holographic M5 branes in AdS7 × S4

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Varun Gupta
Keyword(s):  
General Solution ◽  
Special Class ◽  
Gauge Theories ◽  
Holomorphic Functions ◽  
Boundary Region ◽  
Complex Variables ◽  
Minimal Amount ◽  
World Volume ◽  
The World ◽  
Supersymmetric Gauge

Abstract We study classical M5 brane solutions in the probe limit in the AdS7× S4 background geometry that preserve the minimal amount of supersymmetry. These solutions describe the holography of codimension-2 defects in the 6d boundary dual $$ \mathcal{N} $$ N = (0, 2) supersymmetric gauge theories. The general solution is described in terms of holomorphic functions that satisfy a scaling condition. We show the behavior of the world-volume of a special class of BPS solutions near the AdS boundary region can be characterized by general equations, which describe it as intersections of the zeros of holomorphic functions in three complex variables with a 5-sphere.

scholarly journals THE LARGE-N LIMIT OF $\mathcal{N} = 1$ FIELD THEORIES FROM F THEORY

1999 ◽  
Vol 14 (05) ◽  
pp. 369-378 ◽  
Author(s):  
CHANGHYUN AHN ◽  
KYUNGHO OH ◽  
RADU TATAR
Keyword(s):  
Space Time ◽  
Field Theories ◽  
Text Field ◽  
Large N ◽  
World Volume ◽  
The World

We study AdS/CFT correspondence in four-dimensional [Formula: see text] field theories realized on the world-volume of D3 branes near the intersections between D7 and D 7′ branes in F theory studied by Aharony et al. We consider the compactification of F theory on elliptically fibered Calabi–Yau threefolds corresponding to two sets of parallel D7 branes sharing six space–time directions. This can be viewed as orbifolds of six torus T6 by Zp × Zq(p,q = 2,3,4,6). We find the large-N spectrum of chiral primary operators by exploiting the property of AdS/CFT correspondence. Moreover, we discuss super gravity solutions for D3 branes in D7 and D 7′ branes background.

scholarly journals Local incompressibility of fractional quantum Hall states at a filling factor of 3/2

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
L. V. Kulik ◽  
V. A. Kuznetsov ◽  
A. S. Zhuravlev ◽  
V. Umansky ◽  
I. V. Kukushkin
Keyword(s):  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Hall States

scholarly journals Folding of Hitchin Systems and Crepant Resolutions

2021 ◽  
Author(s):  
Florian Beck ◽  
Ron Donagi ◽  
Katrin Wendland
Keyword(s):  
Fixed Point ◽  
Lie Algebras ◽  
Integrable Systems ◽  
Trace Back ◽  
Dynkin Diagrams ◽  
Or Groups ◽  
Hitchin Systems ◽  
Singular Fibers ◽  
Crepant Resolutions ◽  
Intermediate Jacobian

Abstract Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of $\textrm{ABCDEFG}$-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of $\textrm{ADE}$-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi–Yau orbifold stacks constructed by the 1st author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi–Yau three-folds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.

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