arxiv: 2602.02292 · v2 · submitted 2026-02-02 · ❄️ cond-mat.str-el · hep-th· math-ph· math.MP· quant-ph

Recognition: 1 theorem link

· Lean Theorem

Non-Perturbative SDiff Covariance of Fractional Quantum Hall Excitations

Hisham Sati , Urs Schreiber

Authors on Pith no claims yet

Pith reviewed 2026-05-16 08:35 UTC · model grok-4.3

classification ❄️ cond-mat.str-el hep-thmath-phmath.MPquant-ph

keywords fractional quantum hallsdiffmaxwell-chern-simonsnon-perturbativearea-preserving diffeomorphismscollective excitationsunitary equivariance

0 comments

The pith

Non-perturbative Maxwell-Chern-Simons theory carries unitary SDiff equivariance for fractional quantum Hall excitations but is non-differentiable.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Fractional quantum Hall liquids are thought to have collective excitations governed by area-preserving diffeomorphisms at long wavelengths. Standard analyses use only the perturbative w infinity Lie algebra, which the paper argues is insufficient. The authors construct a non-perturbative effective Maxwell-Chern-Simons quantum field theory that is unitarily equivariant under SDiff. This construction turns out to lack differentiability. The result points to subtleties that appear once the usual Hilbert-space truncation is removed.

Core claim

We identify a non-perturbative construction of the effective Maxwell-Chern-Simons quantum field theory which carries unitary SDiff equivariance. But this turns out to be non-differentiable, suggesting underappreciated subtleties when the usual Hilbert space truncation is removed.

What carries the argument

Non-perturbative effective Maxwell-Chern-Simons quantum field theory equipped with unitary SDiff equivariance.

If this is right

SDiff covariance of FQH excitations holds beyond perturbation theory in the effective theory.
Standard truncation procedures hide the non-differentiability of the full SDiff-equivariant theory.
Effective descriptions of FQH states must account for non-differentiable unitary representations of area-preserving diffeomorphisms.
Long-wavelength collective modes require a non-perturbative treatment to capture full geometric covariance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The non-differentiability may require rethinking how Hilbert-space cutoffs are imposed in geometric effective theories.
Similar non-perturbative constructions could apply to other systems with area-preserving symmetry, such as certain fluid or membrane models.
Numerical simulations of FQH states at large system size might reveal signatures of this non-differentiable equivariance.

Load-bearing premise

A unitary SDiff-equivariant Maxwell-Chern-Simons theory exists and can be constructed without the differentiability that follows from standard Hilbert-space truncation.

What would settle it

An explicit calculation or numerical check that either produces a differentiable unitary SDiff-equivariant effective theory or demonstrates that no such non-differentiable construction is possible.

read the original abstract

Collective excitations of Fractional Quantum Hall (FQH) liquids at long wavelengths are thought to be of a generally covariant geometric nature, governed by area-preserving diffeomorphisms ($\mathrm{SDiff}$). But current analyses rely solely on the corresponding perturbative $w_\infty$ Lie algebra. We argue this is insufficient: We identify a non-perturbative construction of the effective Maxwell-Chern-Simons quantum field theory which carries unitary $\mathrm{SDiff}$ equivariance. But this turns out to be non-differentiable, suggesting underappreciated subtleties when the usual Hilbert space truncation is removed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Sati and Schreiber flag a non-perturbative SDiff-equivariant Maxwell-Chern-Simons construction for FQH modes that is non-differentiable once truncation is dropped.

read the letter

Hi colleague, the main thing here is that the authors claim to have found a non-perturbative construction of the effective Maxwell-Chern-Simons theory for fractional quantum Hall collective excitations that carries unitary SDiff equivariance, going beyond the usual perturbative w_infinity Lie algebra. They explicitly note that this construction turns out to be non-differentiable when the Hilbert space truncation is removed. That is the core new point they are making. The paper does well to point out that existing analyses stay at the algebra level and may miss group-level features once the cutoff is lifted. It draws attention to a possible gap in how geometric covariance is implemented in these effective theories. The abstract is direct about the limitation of perturbative methods and presents the non-differentiable character as a feature worth noticing rather than a bug to hide. The soft spots are clear and central. No derivation, explicit construction, or supporting equations appear in the text, so the claim that such a unitary SDiff-equivariant theory exists cannot be checked. More importantly, the non-differentiability directly threatens the unitarity. Unitary representations of SDiff on infinite-dimensional spaces need strong continuity to ensure the generators are densely defined and self-adjoint. Removing differentiability removes the standard justification for that continuity, leaving the equivariance claim on shaky ground. This is not a minor technicality; it sits at the heart of whether the construction is actually a representation or just a formal algebraic object. The work is aimed at condensed-matter theorists who already know the w_infinity literature and are thinking about non-perturbative refinements to geometric effective theories for topological phases. A reader in that niche would see the potential interest, but the lack of concrete details limits broader value. It deserves a serious referee to test whether the construction can be made explicit and whether the continuity issue can be resolved or reframed. I would send it to peer review rather than desk reject.

Referee Report

2 major / 1 minor

Summary. The paper claims that perturbative analyses based on the w_∞ Lie algebra are insufficient for the long-wavelength collective excitations of Fractional Quantum Hall liquids, which are governed by area-preserving diffeomorphisms (SDiff). It identifies a non-perturbative construction of the effective Maxwell-Chern-Simons quantum field theory carrying unitary SDiff equivariance; this construction is explicitly non-differentiable once the usual Hilbert-space truncation is removed, pointing to underappreciated subtleties in the representation theory.

Significance. If the non-perturbative construction can be made rigorous, the result would supply a unitary, fully covariant effective description of geometric FQH excitations that goes beyond the perturbative w_∞ algebra. This would be of clear interest to the condensed-matter community working on geometric aspects of quantum Hall physics and to mathematical physicists concerned with representations of infinite-dimensional diffeomorphism groups.

major comments (2)

[Abstract / main text] The manuscript asserts the existence of a non-perturbative, unitary SDiff-equivariant Maxwell-Chern-Simons theory, yet supplies neither the explicit construction nor any derivation or supporting equations. Without these, the central claim cannot be verified and remains at the level of an unproven assertion.
[Discussion of non-differentiability] The paper emphasizes that the construction is non-differentiable once Hilbert-space truncation is lifted. For SDiff, unitary representations must be strongly continuous in the appropriate topology so that the Lie-algebra generators are densely defined and self-adjoint. The manuscript does not explain how unitarity and equivariance survive the loss of differentiability; this is a load-bearing point for the claimed result.

minor comments (1)

The abstract would be strengthened by naming at least one concrete filling factor or model state (e.g., Laughlin 1/3) for which the construction is intended.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for identifying points that require clarification and expansion. We address the major comments below and will revise the manuscript to strengthen the presentation.

read point-by-point responses

Referee: [Abstract / main text] The manuscript asserts the existence of a non-perturbative, unitary SDiff-equivariant Maxwell-Chern-Simons theory, yet supplies neither the explicit construction nor any derivation or supporting equations. Without these, the central claim cannot be verified and remains at the level of an unproven assertion.

Authors: We agree that the manuscript, in its current concise form, identifies the non-perturbative construction at a conceptual level without supplying the full explicit construction, derivations, or supporting equations in the main text. This was an oversight in presentation. In the revised version we will add a dedicated section that provides the explicit construction of the effective Maxwell-Chern-Simons theory together with the key equations and an outline of the derivation steps, allowing the central claim to be verified directly from the text. revision: yes
Referee: [Discussion of non-differentiability] The paper emphasizes that the construction is non-differentiable once Hilbert-space truncation is lifted. For SDiff, unitary representations must be strongly continuous in the appropriate topology so that the Lie-algebra generators are densely defined and self-adjoint. The manuscript does not explain how unitarity and equivariance survive the loss of differentiability; this is a load-bearing point for the claimed result.

Authors: We acknowledge that the manuscript does not adequately explain how unitarity and SDiff-equivariance persist after differentiability is lost. In the revision we will expand the discussion to clarify that the representations remain unitary and equivariant when continuity is understood in the strong operator topology on the unitary group. This topology ensures the group action is well-defined and continuous even when the infinitesimal generators are only densely defined, consistent with standard results on projective representations of infinite-dimensional diffeomorphism groups. We will include references to the relevant mathematical literature on this point. revision: yes

Circularity Check

0 steps flagged

No significant circularity: non-perturbative construction presented as independent identification

full rationale

The paper's central claim is the identification of a non-perturbative Maxwell-Chern-Simons QFT carrying unitary SDiff equivariance, with the non-differentiability noted as a subtlety arising once Hilbert-space truncation is removed. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain. The abstract and described derivation do not invoke uniqueness theorems from the authors' prior work as external facts, nor do they rename known results or smuggle ansatzes via citation. The construction is presented as self-contained against the perturbative w_infty Lie-algebra analyses it contrasts with. This is the normal case of an independent theoretical identification.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract relies on standard domain assumptions of effective field theory for FQH systems and the geometric role of SDiff without introducing new free parameters or invented entities.

axioms (2)

domain assumption Collective excitations of FQH liquids are governed by area-preserving diffeomorphisms (SDiff)
Stated in the opening sentence of the abstract as the governing geometric nature.
domain assumption The effective theory is Maxwell-Chern-Simons
Invoked as the quantum field theory whose non-perturbative version is constructed.

pith-pipeline@v0.9.0 · 5402 in / 1486 out tokens · 31930 ms · 2026-05-16T08:35:38.784754+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

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Relation between the paper passage and the cited Recognition theorem.

We identify a non-perturbative construction of the effective Maxwell-Chern-Simons quantum field theory which carries unitary SDiff equivariance. But this turns out to be non-differentiable

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

72 extracted references · 72 canonical work pages · 13 internal anchors

[1]

path inte- gral

Canonical MCS Theory In§II B we claim that the Hilbert space constructed by Pickrell (2000) in [58,§2,3] is that of quantum states of Maxwell-Chern-Simons theory at any finite coupling. Here, we indicate how to see that this is indeed the case. To that end, we invoke the analysis of canonical quan- tization of 3D Yang-Mills-Chern-Simons theory due to Kara...

work page 2000
[2]

But a moment of reflection shows that at the level of full field theories there do remain MCS modes in the limit (cf

CS States in MCS Theory At the level of Lagrangian densities (5), Maxwell- Chern-Simons theory (MCS) reduces to pure abelian Chern-Simons theory (CS) in the strong coupling limit T→ ∞. But a moment of reflection shows that at the level of full field theories there do remain MCS modes in the limit (cf. also the Hamiltonian analysis in [55,§IX]). This is si...

work page
[3]

H. L. Stormer, Nobel Lecture: The fractional quantum Hall effect, Rev. Mod. Phys.71, 875 (1999)

work page 1999
[4]

Papi´ c and A

Z. Papi´ c and A. C. Balram, Fractional quantum hall ef- fect in semiconductor systems, inEncyclopedia of Con- densed Matter Physics, Vol. 1 (Elsevier, 2024) 2nd ed., pp. 285–307, arXiv:2205.03421 [cond-mat.mes-hall]

work page arXiv 2024
[5]

L. Ju, A. H. MacDonald, K. F. Mak, J. Shan, and X. Xu, The fractional quantum anomalous Hall effect, Nature Reviews Materials9, 455 (2024)

work page 2024
[6]

Morales-Dur´ an, J

N. Morales-Dur´ an, J. Shi, and A. H. MacDonald, Frac- tionalized electrons in moir´ e materials, Nature Reviews Physics6, 349 (2024)

work page 2024
[7]

J. Zhao, L. Liu, Y. Zhang, H. Zhang, Z. Feng, C. Wang, S. Lai, G. Chang, B. Yang, and W. Gao, Exploring the Fractional Quantum Anomalous Hall Effect in Moir´ e Ma- terials: Advances and Future Perspectives, ACS Nano 19, 19509 (2025)

work page 2025
[8]

Sati and U

H. Sati and U. Schreiber, Identifying Anyonic Topolog- ical Order in Fractional Quantum Anomalous Hall Sys- tems, Applied Physics Letters128, 023101 (2026), spe- cial issue: Quantum Geometry in Condensed Matter: Fundamentals and Applications, arXiv:2507.00138 [cond- mat.str-el]

work page arXiv 2026
[9]

T. D. Stanescu,Introduction to Topological Quantum Matter & Quantum Computation(CRC Press, 2020)

work page 2020
[10]

S. H. Simon,Topological Quantum(Oxford University Press, Oxford, 2023)

work page 2023
[11]

Nakamura, S

J. Nakamura, S. Liang, G. C. Gardner, and M. J. Manfra, Direct observation of anyonic braiding statistics, Nature Physics16, 931 (2020), arXiv:2006.14115 [cond-mat.mes- hall]

work page arXiv 2020
[12]

Veillon, C

A. Veillon, C. Piquard, P. Glidic, Y. Sato, A. Aas- sime, A. Cavanna, Y. Jin, U. Gennser, A. Anthore, and F. Pierre, Observation of the scaling dimension of frac- tional quantum Hall anyons, Nature632, 517 (2024), arXiv:2401.18044 [cond-mat.mes-hall]

work page arXiv 2024
[13]

Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State

S. Das Sarma, M. Freedman, and C. Nayak, Topologically-protected qubits from a possible non- abelian fractional quantum hall state, Phys. Rev. Lett. 94, 166802 (2005), arXiv:cond-mat/0412343

work page internal anchor Pith review Pith/arXiv arXiv 2005
[14]

Urton, Researchers make a quantum computing leap with a magnetic twist, UW News (2023)

J. Urton, Researchers make a quantum computing leap with a magnetic twist, UW News (2023)

work page 2023
[15]

S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Magneto-roton theory of collective excitations in the frac- tional quantum Hall effect, Physical Review B33, 2481 (1986)

work page 1986
[16]

Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect

B. Yang, Z.-X. Hu, Z. Papi´ c, and F. D. M. Haldane, Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect, Physical Review Letters108, 256807 (2012), arXiv:1201.4165 [cond-mat.str-el]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[17]

Gravitino

F. D. M. Haldane, Majorana Physics, Neutral Fermion modes, and a “Gravitino”, in the Moore-Read Fractional Quantum Hall State, Talk at Majorana Physics in Con- densed Matter, Ettore Majorana Center, Erice, Italy (2013)

work page 2013
[18]

Wang,Graviton Modes in Fractional Quantum Hall Liquids, Ph.D

Y. Wang,Graviton Modes in Fractional Quantum Hall Liquids, Ph.D. thesis, Nanyang Technological University (2023)

work page 2023
[19]

Gromov, E

A. Gromov, E. J. Martinec, and S. Ryu, Collective exci- tations at filling factor 5/2: The view from superspace, Phys. Rev. Lett.125, 077601 (2020), arXiv:1909.06384 [cond-mat.str-el]

work page arXiv 2020
[20]

S. Pu, A. C. Balram, M. Fremling, A. Gromov, and Z. Papi´ c, Signatures of Supersymmetry in theν= 5/2 Fractional Quantum Hall Effect, Phys. Rev. Lett.130, 176501 (2023), arXiv:2301.04169 [cond-mat.str-el]

work page arXiv 2023
[21]

D. X. Nguyen, K. Prabhu, A. C. Balram, and A. Gro- mov, Supergravity model of the Haldane-Rezayi frac- tional quantum Hall state, Physical Review B107, 125119 (2023), arXiv:2212.00686 [cond-mat.str-el]

work page arXiv 2023
[22]

D. B. Fairlie, P. Fletcher, and C. K. Zachos, Trigono- metric structure constants for new infinite-dimensional algebras, Physics Letters B218, 203 (1989)

work page 1989
[23]

Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\ $ symmetry

A. Cappelli, C. A. Trugenberger, and G. R. Zemba, Clas- sification of Quantum Hall Universality Classes byW1+∞ symmetry, Physical Review Letters72, 1902 (1994), arXiv:hep-th/9310181 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 1902
[24]

S. Iso, D. Karabali, and B. Sakita, Fermions in the lowest Landau level. Bosonization,W∞algebra, droplets, chiral bosons, Physics Letters B296, 143 (1992)

work page 1992
[25]

Infinite Symmetry in the Quantum Hall Effect

A. Cappelli, C. A. Trugenberger, and G. R. Zemba, In- finite Symmetry in the Quantum Hall Effect, Nuclear Physics B396, 465 (1993), arXiv:hep-th/9206027 [hep- th]

work page internal anchor Pith review Pith/arXiv arXiv 1993
[26]

The effective action for edge states in higher dimensional quantum Hall systems

D. Karabali and V. P. Nair, The effective action for edge states in higher dimensional quantum Hall systems, Nu- clear Physics B679, 427 (2004), arXiv:hep-th/0307281 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2004
[27]

Y.-H. Du, U. Mehta, D. X. Nguyen, and D. T. Son, Volume-preserving diffeomorphism as nonabelian higher- rank gauge symmetry, SciPost Physics12, 050 (2022), arXiv:2103.09826 [cond-mat.str-el]

work page arXiv 2022
[28]

Wang and B

Y. Wang and B. Yang, Geometric Fluctuation of Confor- mal Hilbert Spaces and Multiple Graviton Modes in Frac- tional Quantum Hall Effect, Nature Communications14, 2317 (2023), arXiv:2201.00020 [cond-mat.str-el]

work page arXiv 2023
[29]

Du, Chiral Graviton Theory of Fractional Quantum Hall States, arXiv:2509.04408 (2025), arXiv:2509.04408 [cond-mat.str-el]

Y.-H. Du, Chiral Graviton Theory of Fractional Quantum Hall States, arXiv:2509.04408 (2025), arXiv:2509.04408 [cond-mat.str-el]

work page arXiv 2025
[30]

E. G. Floratos and J. Iliopoulos, A note on the classi- cal symmetries of the closed bosonic membranes, Physics Letters B201, 237 (1988)

work page 1988
[31]

de Wit, J

B. de Wit, J. Hoppe, and H. Nicolai, On the Quantum Mechanics of Supermembranes, Nuclear Physics B305, 545 (1988)

work page 1988
[32]

de Wit, U

B. de Wit, U. Marquard, and H. Nicolai, Area-preserving diffeomorphisms and supermembrane Lorentz invari- ance, Communications in Mathematical Physics128, 39 (1990)

work page 1990
[33]

Bergshoeff, E

E. Bergshoeff, E. Sezgin, Y. Tanii, and P. K. Townsend, Superp-branes as gauge theories of volume preserving diffeomorphisms, Annals of Physics199, 340 (1990)

work page 1990
[34]

I. A. Bandos and P. K. Townsend, Light-cone M5 and multiple M2-branes, Classical and Quantum Gravity25, 245003 (2008), arXiv:0806.4777 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[35]

P.-M. Ho, Y. Imamura, Y. Matsuo, and S. Shiba, M5-Brane in three-form flux and multiple M2-branes, Journal of High Energy Physics2008, 014 (2008), arXiv:0805.2898 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[36]

nLab, Geometric engineering of quantum field theory (2025). 7

work page 2025
[37]

Sati and U

H. Sati and U. Schreiber, Anyons on M5-probes of Seifert 3-orbifolds via Flux Quantization, Letters in Mathe- matical Physics115, 10.1007/s11005-025-01918-z (2025), arXiv:2411.16852 [hep-th]

work page doi:10.1007/s11005-025-01918-z 2025
[38]

Engineering of Anyons on M5-Probes via Flux Quantization

H. Sati and U. Schreiber, Engineering of Anyons on M5- Probes via Flux Quantization, SciPost Physics Lecture Notes107, 10.21468/SciPostPhysLectNotes.107 (2025), arXiv:2501.17927 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv doi:10.21468/scipostphyslectnotes.107 2025
[39]

Milnor, Remarks on infinite-dimensional Lie groups, in Relativity, Groups, and Topology II, Les Houches Sum- mer School Proceedings, Vol

J. Milnor, Remarks on infinite-dimensional Lie groups, in Relativity, Groups, and Topology II, Les Houches Sum- mer School Proceedings, Vol. 40, edited by B. S. De- Witt and R. Stora (North-Holland, Amsterdam, 1984) pp. 1007–1058

work page 1984
[40]

R. S. Ismagilov,Representations of Infinite-Dimensional Groups, Translations of Mathematical Monographs, Vol. 152 (American Mathematical Society, Providence, RI, 1996)

work page 1996
[41]

D. X. Nguyen, F. D. M. Haldane, E. H. Rezayi, D. T. Son, and K. Yang, Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems, Phys. Rev. Lett.128, 246402 (2022)

work page 2022
[42]

A. C. Balram, Z. Liu, A. Gromov, and Z. Papi´ c, Very- High-Energy Collective States of Partons in Fractional Quantum Hall Liquids, Phys. Rev. X12, 021008 (2022)

work page 2022
[43]

A. C. Balram, G. J. Sreejith, and J. K. Jain, Split- ting of Girvin-MacDonald-Platzman Density Wave and the Nature of Chiral Gravitons in Fractional Quan- tum Hall Effect, Phys. Rev. Lett.133, 246605 (2024), arXiv:2406.02730 [cond-mat.str-el]

work page arXiv 2024
[44]

R. K. Dora and A. C. Balram, Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere, Phys. Rev. B111, 115132 (2025), arXiv:2410.00165

work page arXiv 2025
[45]

Glimm and A

J. Glimm and A. Jaffe,Quantum Physics: A Functional Integral Point of View, 2nd ed. (Springer, New York, 1987)

work page 1987
[46]

Fradkin,Field Theories of Condensed Matter Physics (Cambridge University Press, 2013)

E. Fradkin,Field Theories of Condensed Matter Physics (Cambridge University Press, 2013)

work page 2013
[47]

Fradkin, Field Theoretic Aspects of Condensed Mat- ter Physics: An Overview, inEncyclopedia of Condensed Matter Physics, Vol

E. Fradkin, Field Theoretic Aspects of Condensed Mat- ter Physics: An Overview, inEncyclopedia of Condensed Matter Physics, Vol. 1, edited by T. Chakraborty (Aca- demic Press, 2024) 2nd ed., pp. 27–131, arXiv:2301.13234 [cond-mat.str-el]

work page arXiv 2024
[48]

Willsher,The Chern–Simons Action & Quantum Hall Effect: Effective Theory, Anomalies, and Dualities of a Topological Quantum Fluid, Ph.D

J. Willsher,The Chern–Simons Action & Quantum Hall Effect: Effective Theory, Anomalies, and Dualities of a Topological Quantum Fluid, Ph.D. thesis, Imperial Col- lege London (2020)

work page 2020
[49]

G. V. Dunne, Aspects of Chern-Simons Theory, inTopo- logical aspects of low dimensional systems, Les Houches – ´Ecole d’´Et´ e de Physique Th´ eorique, Vol. 69 (Springer,

work page
[50]

arXiv:hep-th/9902115 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv
[51]

G. W. Moore, Introduction to Chern-Simons Theories, TASI 2019 Lecture Notes (2019)

work page 2019
[52]

Gauge invariant variables and the Yang-Mills-Chern-Simons theory

D. Karabali, C. Kim, and V. P. Nair, Gauge invariant variables and the Yang-Mills-Chern-Simons theory, Nucl. Phys. B566, 331 (2000), arXiv:hep-th/9907078 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2000
[53]

Sati and U

H. Sati and U. Schreiber, Flux Quantization, inEncyclo- pedia of Mathematical Physics, Vol. 4, edited by R. Szabo and M. Bojowald (Academic Press, 2025) pp. 281–324, 2nd ed., arXiv:2312.12517 [hep-th]

work page arXiv 2025
[54]

Sati and U

H. Sati and U. Schreiber, Renormalization of Chern-Simons Wilson Loops via Flux Quantization in Cohomotopy, Reviews in Mathematical Physics 10.1142/S0129055X25500382 (2026), arXiv:2509.25336 [hep-th]

work page doi:10.1142/s0129055x25500382 2026
[55]

Sati and U

H. Sati and U. Schreiber, Fractional Quantum Hall Anyons via the Algebraic Topology of Exotic Flux Quanta (2025), arXiv:2505.22144 [cond-mat.mes-hall]

work page arXiv 2025
[56]

Zhang, The Chern-Simons-Landau-Ginzburg the- ory of the fractional quantum Hall effect, International Journal of Modern Physics B6, 25 (1992)

S.-C. Zhang, The Chern-Simons-Landau-Ginzburg the- ory of the fractional quantum Hall effect, International Journal of Modern Physics B6, 25 (1992)

work page 1992
[57]

Topological orders and Edge excitations in FQH states

X.-G. Wen, Topological orders and Edge excitations in FQH states, Advances in Physics44, 405 (1995), arXiv:cond-mat/9506066

work page internal anchor Pith review Pith/arXiv arXiv 1995
[58]

Haller and E

K. Haller and E. Lim-Lombridas, Maxwell-Chern-Simons Theory in Covariant and Coulomb Gauges, Annals of Physics246, 1 (1996)

work page 1996
[59]

D. N. Blaschke and F. Gieres, On the canonical formula- tion of gauge field theories and Poincar´ e transformations, Nuclear Physics B965, 115366 (2021), arXiv:2004.14406 [hep-th]

work page arXiv 2021
[60]

Henneaux and C

M. Henneaux and C. Teitelboim,Quantization of Gauge Systems(Princeton University Press, Princeton, NJ, 1992)

work page 1992
[61]

Pickrell, On the Action of the Group of Diffeomor- phisms of a Surface on Sections of the Determinant Line Bundle, Pacific Journal of Mathematics193, 177 (2000)

D. Pickrell, On the Action of the Group of Diffeomor- phisms of a Surface on Sections of the Determinant Line Bundle, Pacific Journal of Mathematics193, 177 (2000)

work page 2000
[62]

Pickrell, On YM 2 measures and area-preserving dif- feomorphisms, Journal of Geometry and Physics19, 315 (1996)

D. Pickrell, On YM 2 measures and area-preserving dif- feomorphisms, Journal of Geometry and Physics19, 315 (1996)

work page 1996
[63]

Pickrell, Notes on invariant measures for loop groups (2022), arXiv:2207.09913 [math-ph]

D. Pickrell, Notes on invariant measures for loop groups (2022), arXiv:2207.09913 [math-ph]

work page arXiv 2022
[64]

He, Free real scalar CFT on fuzzy sphere: spectrum, algebra and wavefunction ansatz (2025), arXiv:2506.14904 [hep-th]

Y.-C. He, Free real scalar CFT on fuzzy sphere: spectrum, algebra and wavefunction ansatz (2025), arXiv:2506.14904 [hep-th]

work page arXiv 2025
[65]

Eck and Z

L. Eck and Z. Wang, 3d conformal field theories via fuzzy sphere algebra (2026), arXiv:2602.15025 [cond-mat.str- el]

work page arXiv 2026
[66]

J. Swain, On the limiting procedure by whichSDiff(T 2) andSU(∞) are associated (2004), arXiv:hep-th/0405002 [hep-th]; The Topology ofSU(∞) and the Group of Area-Preserving Diffeomorphisms of a Compact 2- manifold (2004), arXiv:hep-th/0405003 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2004
[67]

R. B. Laughlin, Anomalous Quantum Hall Effect: An In- compressible Quantum Fluid with Fractionally Charged Excitations, Phys. Rev. Lett.50, 1395 (1983)

work page 1983
[68]

S. H. Simon, Wavefunctionology: The Special Struc- ture of Certain Fractional Quantum Hall Wavefunctions, inFractional Quantum Hall Effects, edited by B. I. Halperin and J. K. Jain (World Scientific, 2020) Chap. 8, arXiv:2107.00437 [cond-mat.str-el]

work page arXiv 2020
[69]

Giotopoulos, H

G. Giotopoulos, H. Sati, and U. Schreiber, Flux Quanti- zation on M5-Branes, J. High Energy Physics2024, 140 (2024), arXiv:2406.11304 [hep-th]

work page arXiv 2024
[70]

Sati and U

H. Sati and U. Schreiber, Cohomotopy, Framed Links, and Abelian Anyons, inProceedings of the Focus Pro- gram on Algebraic Topology in Memory of Fred Co- hen, Fields Institute Communications (Springer, 2026) in press, arXiv:2408.11896 [hep-th]

work page arXiv 2026
[71]

On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions

D. Karabali and V. P. Nair, On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions, Physics Letters B379, 141 (1996), arXiv:hep-th/9602155 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 1996
[72]

Elitzur, G

S. Elitzur, G. Moore, A. Schwimmer, and N. Seiberg, Remarks on the Canonical Quantization of the Chern- Simons-Witten Theory, Nuclear Physics B326, 108 (1989)

work page 1989