Fractional quantum Hall effect on the two-sphere: A matrix model proposal

Morariu, Bogdan; Polychronakos, Alexios P.

doi:10.1103/physrevd.72.125002

Cited by 13 publications

(13 citation statements)

References 45 publications

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“…Properties of such theories on flat noncommutative spaces are fairly well understood by now. They have also been formulated on some (2 + 1)-dimensional fuzzy spaces, but a general formulation on fuzzy spaces has not yet been possible [42]. These theories are matrix versions of the Chern-Simons theory characterized by the choice of the fuzzy space and the gauge group and give the usual Chern-Simons theory at large N , just as the action (92) does.…”

Section: Discussion Outlookmentioning

confidence: 99%

Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry

Karabali¹,

Nair²

2006

J. Phys. A: Math. Gen.

105

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We give a brief review of quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a onedimensional matrix action whose large N limit produces an effective action describing the gauge interactions of a higher dimensional quantum Hall droplet. The bulk action is a Chern-Simons type term whose anomaly is exactly cancelled by the boundary action given in terms of a chiral, gauged Wess-Zumino-Witten theory suitably generalized to higher dimensions. We argue that the gauge fields in the Chern-Simons action can be understood as parametrizing the different ways in which the large N limit of the matrix theory is taken.The possible relevance of these ideas to fuzzy gravity is explained. Other applications are also briefly discussed.

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Section: Discussion Outlookmentioning

confidence: 99%

Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry

Karabali¹,

Nair²

2006

J. Phys. A: Math. Gen.

105

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“…In the SVM classifier, we have decided to use both polynomial and Gaussian kernels as it was presented in [9]. The results obtained using the SVM classifier and all 27240 features are presented in the Table 2.…”

Section: Obtained Results With Svm Classifiermentioning

confidence: 99%

“…In this new representation each vector in the hyper-vector space represents a part of speech component. We want to compare the results of the new representation with the results obtained by us in previous experiments where documents were represented only by frequencies of words vectors [9]. We have used the Support Vector Machine (SVM) algorithm for classifying text documents.…”

Section: Tagging the Reuters Datasetmentioning

confidence: 99%

An Extension of the VSM Documents Representation

Vintan

Morariu

Cretulescu

et al. 2017

INT J COMPUT COMMUN

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In this paper we will present a new approach regarding the documents representation in order to be used in classification and/or clustering algorithms. In our new representation we will start from the classical "bag-of-words" representation but we will augment each word with its correspondent part-of-speech. Thus we will introduce a new concept called hyper-vectors where each document is represented in a hyper-space where each dimension is a different part-of-speech component. For each dimension the document is represented using the Vector Space Model (VSM). In this work we will use only five different parts of speech: noun, verb, adverb, adjective and others. In the hyper-space each dimension has a different weight. To compute the similarity between two documents we have developed a new hyper-cosine formula. Some interesting classification experiments are presented as validation cases.

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“…To that purpose, one should first identify the matrix model regularization of the continuous field theory developed in this paper. This may be done by extending the results of [13,14] obtained in the framework of fractional quantum Hall droplets. An attempt using matrix field variables valued in GL (N, C) representations is under study in [15], progress in this direction will be reported elsewhere.…”

Section: Discussionmentioning

confidence: 99%

“…transforming as isodoublets under SL (2) isometry, the coordinates of a given D string moving in conifold is given by the holomorphic field doublets, 13) with the local constraint eqs, 14) and the projective symmetry…”

Section: Fluid Approximationmentioning

confidence: 99%

D-string fluid in conifold, I: Topological gauge model

Laamara¹,

Drissi²,

Saidi³

2006

Nuclear Physics B

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Motivated by similarities between quantum Hall systemsà la Susskind and aspects of topological string theory on conifold as well as results obtained in hepth/0601020, we study the dynamics of D-string fluids running in deformed conifold in presence of a strong and constant RR background B-field. We first introduce the basis of D-string system in fluid approximation and then derive the holomorphic non commutative gauge invariant field action describing its dynamics in conifold.This study may be also viewed as embedding Susskind description for Laughlin liquid in type IIB string theory. FQH systems on real manifolds R × S 2 and S 3 are shown to be recovered by restricting conifold to its Lagrangian sub-manifolds.Aspects of quantum behaviour of the string fluid are discussed.

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Fractional quantum Hall effect on the two-sphere: A matrix model proposal

Cited by 13 publications

References 45 publications

Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry

Quantum Hall effect in higher dimensions, matrix models and fuzzy geometry

An Extension of the VSM Documents Representation

D-string fluid in conifold, I: Topological gauge model

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