Quantum Hall Effect in Higher Dimensions

Dimitra Karabali; V.P. Nair

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Quantum Hall Effect in Higher Dimensions

Dimitra Karabali, V.P. Nair

High Energy Physics - Theory · Submitted 28 Mar 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Unlike the case of $S^4$, a finite spatial density can be obtained with a finite number of internal states for each particle.

how it is stated · asserted 1.00 read the record →

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,229 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.93 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of ${\bf C}P^2$ in some detail considering both Abelian and nonabelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of ${\bf C}P^3$ is related to the case of $S^4$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces.	contribution 0.91	0.91	0.11	asserted 1.00
s1	Unlike the case of $S^4$, a finite spatial density can be obtained with a finite number of internal states for each particle.	result 0.99	0.81	0.42	asserted 1.00
s2	We treat the case of ${\bf C}P^2$ in some detail considering both Abelian and nonabelian background fields.	contribution 0.95	0.92	0.07	asserted 0.92
s3	The wavefunctions are obtained and incompressibility of the Hall states is shown.	result 0.90	0.94	0.19	asserted 1.00
s4	The case of ${\bf C}P^3$ is related to the case of $S^4$.	contribution 0.67	0.69	0.05	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of ${\bf C}P^2$ in some detail considering both Abelian and nonabelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of ${\bf C}P^3$ is related to the case of $S^4$.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

6D Fractional Quantum Hall Effect
hep-th 2017-08 conditional novelty 6.0 of 10

A 7D Chern-Simons-like theory of abelian three-form potentials produces fractional quantum Hall physics on its 6D boundary, with continued fractions playing the role of filling fractions.
Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
hep-th 2017-04 conditional novelty 6.0 of 10

Generalized fuzzy four-spheres with twisted extra dimensions solve effective Yang-Mills matrix-model equations, with a speculative link to three particle generations.
Wave Functions and Yukawa Couplings in Local String Compactifications
hep-th 2008-07 conditional novelty 5.0 of 10

Explicit local metrics on P1 x P1 and P2 allow analytic chiral wavefunctions and triple-overlap Yukawa couplings, and reveal that Abelian flux on P2 gives vanishing Yukawas, motivating non-Abelian bundles.
Transgression branes in seven dimensions
hep-th 2026-11 conditional novelty 4.0 of 10

A seven-dimensional transgression action with SO(8) or SO(6,2) gauge group yields brane solutions analogous to Nepomechie-Wu-Zee anyon models, with constant-curvature black-hole metrics providing static Lorentzian solutions.
Lectures on Fuzzy and Fuzzy SUSY Physics
hep-th 2005-11 conditional novelty 3.0 of 10

The notes compile and explain fuzzy sphere and fuzzy supersphere constructions, star products, gauge fields, Dirac operators, anomalies, and exact fuzzy supersymmetry.

How the literature uses it

26 arXiv papers cite this in 45 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 27 sentences without a confident label

Compares with it 1 paper

We shall compare our results for $P^1$ with those of [ref] , by finding explicit solutions of the Dirac equation.

Wave Functions and Yukawa Couplings in Local String Compactifications · Compactification on $P^1$ · 0.97

Cites it as background 13 papers

In parallel, the NCG associated with Landau models has been extensively investigated over for more than two decades [ref] .

Super Landau Model and Howe Duality: From Supermonopole Harmonics to Quantum Matrix Geometry · Introduction · 0.99
Recall that QHE in higher dimensions has been first considered in [ref] for the case of the 4-sphere and has been further developed in [ref] and refs therein for other higher D- manifolds.

Anomalous Quantum Hall Effect of 4D Graphene in Background Fields · Introduction · 0.96
The coset space structure of $CP^k$ spaces has been extensively used to study the integer quantum Hall effect on $CP^1$ [ref] and higher dimensional projective spaces [ref] .

Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect · Introduction and Summary · 0.85

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