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arxiv: 2606.21494 · v1 · pith:S4VXPBIRnew · submitted 2026-06-19 · ✦ hep-th

Non-relativistic limits of mathcal N=4 supersymmetric Yang-Mills theory and S-duality

Hyungrok Kim , Joseph Smith This is my paper

Pith reviewed 2026-06-26 13:38 UTC · model grok-4.3

classification ✦ hep-th
keywords non-relativistic limitsN=4 supersymmetric Yang-MillsS-dualityGalilean Yang-MillsBPS monopolesmoduli spacePSL(2,Z) dualitytopological deformations
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The pith

Non-relativistic limits of N=4 supersymmetric Yang-Mills theory form a three-dimensional moduli space on which PSL(2,Z) dualities act more richly than in the relativistic theory.

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

The paper constructs a family of non-relativistic limits of four-dimensional maximally supersymmetric Yang-Mills theory from a Type IIB brane configuration with a D3-brane and (p,q)-strings. These limits yield topological deformations of supersymmetric Galilean Yang-Mills theory, featuring a theta-term and monopole charge coupling, or of quantum mechanics on the BPS monopole moduli space, featuring only a theta-term. The resulting theories assemble into a three-dimensional moduli space with nontrivial topology. On this space, PSL(2,Z)-valued dualities operate in a richer and more complex way than in the relativistic parent theory, established directly by path integral in the Abelian case and supported by spectrum and symmetry matching in the non-Abelian case.

Core claim

The family of non-relativistic limits of 4d MSYM obtained from the D3-brane and (p,q)-string setup are topological deformations of supersymmetric Galilean Yang-Mills theory or of quantum mechanics on the moduli space of BPS monopoles. These theories fit together into a three-dimensional moduli space with nontrivial topology, on which PSL(2,Z)-valued dualities act in a richer and more complex way than in the relativistic parent theory. In the Abelian case duality is established directly using the path integral; in the non-Abelian case it is supported by matching the one-particle spectrum as well as the Galilean spacetime symmetries and electric/magnetic invertible one-form symmetries.

What carries the argument

Three-dimensional moduli space of non-relativistic theories with nontrivial topology on which PSL(2,Z)-valued dualities act.

If this is right

  • The deformations consist of a theta-term plus monopole charge coupling for Galilean Yang-Mills and a theta-term alone for the moduli-space quantum mechanics.
  • PSL(2,Z) dualities on the three-dimensional moduli space are richer and more complex than the SL(2,Z) S-duality of the relativistic theory.
  • In the Abelian case the duality holds directly by path-integral computation.
  • In the non-Abelian case the duality is consistent with the one-particle spectrum and with preservation of Galilean spacetime symmetries together with electric and magnetic invertible one-form symmetries.

Where Pith is reading between the lines

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

  • The richer action of duality on the non-relativistic moduli space may produce new protected quantities or invariants unavailable in the relativistic setting.
  • The construction suggests that similar brane-derived non-relativistic limits could be taken in other supersymmetric gauge theories to generate analogous moduli spaces.
  • If the topology of the three-dimensional space controls the duality orbits, one could search for fixed points or special loci where additional symmetries emerge.

Load-bearing premise

The Type IIB brane set-up with a D3-brane and (p,q)-strings correctly realizes the non-relativistic limits of 4d MSYM theory and produces only the stated topological deformations.

What would settle it

A mismatch in the one-particle spectrum or failure of the Galilean spacetime symmetries and electric/magnetic one-form symmetries to match under the proposed duality map in the non-Abelian case.

read the original abstract

We investigate non-relativistic limits of four-dimensional maximally supersymmetric Yang-Mills theory (4d MSYM) and their relation to the nonperturbative $\operatorname{SL}(2;\mathbb Z)$ S-duality of the relativistic theory. We construct a general family of non-relativistic limits using a Type IIB brane set-up with a D3-brane and $(p,q)$-strings and show that the resulting theories are topological deformations of supersymmetric Galilean Yang-Mills theory or quantum mechanics on the moduli space of BPS monopoles. The deformations of the Galilean Yang-Mills theory are the familiar $\theta$-term and a coupling to the monopole charge, while in the moduli space theory the only deformation is a $\theta$-term. This family of theories fit together into a three-dimensional moduli space with nontrivial topology, on which $\operatorname{PSL}(2;\mathbb Z)$-valued dualities act in a richer and more complex way than in the relativistic parent theory. In the Abelian case, we establish the duality directly using the path integral, while in the non-Abelian case we support our claim by matching the one-particle spectrum as well as the Galilean spacetime symmetries and electric/magnetic invertible one-form symmetries.

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.

Referee Report

1 major / 1 minor

Summary. The manuscript constructs non-relativistic limits of four-dimensional N=4 supersymmetric Yang-Mills theory via a Type IIB brane setup with a D3-brane and (p,q)-strings. These limits are identified as topological deformations (a theta-term plus monopole-charge coupling) of supersymmetric Galilean Yang-Mills theory or of quantum mechanics on the BPS monopole moduli space. The resulting family of theories is organized into a three-dimensional moduli space of nontrivial topology on which PSL(2,Z)-valued dualities act more richly than in the relativistic parent theory. Duality is established directly via the path integral in the Abelian case and supported by one-particle spectrum matching together with Galilean spacetime symmetries and electric/magnetic invertible one-form symmetries in the non-Abelian case.

Significance. If the brane-construction identification holds, the work supplies a concrete realization of S-duality in a non-relativistic setting and exhibits a three-dimensional moduli space whose duality action is genuinely richer than the relativistic SL(2,Z) action. The explicit Abelian path-integral argument and the non-Abelian matching of spectra plus symmetries constitute tangible support. The paper is credited for cleanly separating the Abelian and non-Abelian regimes and for using the brane construction to generate the family of deformations.

major comments (1)
  1. [Brane construction (abstract and §2)] The identification that the Type IIB D3-brane plus (p,q)-string configuration yields precisely the claimed topological deformations (theta-term and monopole-charge coupling) with no additional Galilean-invariant operators and with full decoupling of relativistic degrees of freedom is load-bearing for the three-dimensional moduli space and its PSL(2,Z) action. The abstract states that the setup produces only the stated deformations, yet an explicit check that (p,q)-strings induce no non-topological effects would be required to secure the downstream claims.
minor comments (1)
  1. The abstract refers to 'matching the one-particle spectrum' without indicating the section in which the explicit matching tables or equations appear; a forward reference would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the single major comment below and will revise the paper accordingly.

read point-by-point responses

  1. Referee: [Brane construction (abstract and §2)] The identification that the Type IIB D3-brane plus (p,q)-string configuration yields precisely the claimed topological deformations (theta-term and monopole-charge coupling) with no additional Galilean-invariant operators and with full decoupling of relativistic degrees of freedom is load-bearing for the three-dimensional moduli space and its PSL(2,Z) action. The abstract states that the setup produces only the stated deformations, yet an explicit check that (p,q)-strings induce no non-topological effects would be required to secure the downstream claims.

    Authors: We agree that the brane construction is foundational and that the abstract claim requires careful justification. In §2 we derive the effective action by taking the non-relativistic scaling limit of the D3-brane world-volume theory in the presence of (p,q)-strings; the strings source the axio-dilaton background, which produces the topological θ-term, and their magnetic flux produces the monopole-charge coupling. Any additional operators generated by the strings either violate the preserved Galilean and supersymmetry algebra or are suppressed by positive powers of the speed of light and therefore decouple in the limit. Nevertheless, we acknowledge that a more explicit enumeration of possible Galilean-invariant operators and a direct demonstration that none are induced would strengthen the argument. In the revised manuscript we will add a short subsection (or appendix) that performs this check by listing the lowest-dimension Galilean-invariant operators compatible with the symmetries and showing they are absent from the brane-derived action at leading order. This revision will make the identification fully explicit without altering the main results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations rely on direct path-integral and matching arguments

full rationale

The abstract states that Abelian duality is established directly via the path integral and non-Abelian claims are supported by explicit one-particle spectrum matching plus symmetry matching. No load-bearing self-citations, self-definitional steps, or fitted inputs renamed as predictions are indicated in the provided text. The Type IIB brane setup is presented as a construction input whose output is then analyzed, rather than a result derived from the target moduli-space structure. This is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract does not mention any free parameters, axioms, or invented entities; the work appears to rely on standard Type IIB brane constructions without introducing new ones.

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Reference graph

Works this paper leans on

50 extracted references · 40 canonical work pages · 15 internal anchors

  1. [1]

    Non-relativistic intersecting branes, Newton-Cartan geometry and AdS/CFT

    Neil Lambert and Joseph Smith. Non-relativistic intersecting branes, Newton-Cartan geometry and AdS/CFT. Journal of High Energy Physics, 2024(07):224, July 2024. arXiv:2405.06552, doi:10.1007/JHEP07(2024) 224

    work page doi:10.1007/jhep07(2024 2024

  2. [2]

    Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory

    James M. Drummond, Johannes M. Henn, Gregory Petrovich Korchemsky (Григорий Петрович Корчемский) , and Emery Simeonov Sokatchev (Емери Симеонов Сокачев) . Dual superconformal symmetry of scattering amplitudes in 𝒩 = 4 super-Yang–Mills theory. Nuc- lear Physics B, 828(1–2):317–374, March 2010. arXiv:0807.1095, doi: 10.1016/j.nuclphysb.2009.11.022

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.nuclphysb.2009.11.022 2010

  3. [3]

    Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory

    James M. Drummond, Johannes M. Henn, and Jan Plefka. Yangian symmetry of scattering amplitudes in𝒩 = 4 super Yang-Mills theory. Journal of High Energy Physics, 2009(05):046, May 2009. arXiv:0902.2987, doi:10.1088/1126-6708/2009/05/046. 31

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1126-6708/2009/05/046 2009

  4. [4]

    Generalized Global Symmetries

    Davide Silvano Achille Gaiotto, Anton Nikolaevich Kapustin (Антон Нико- лаевич Капустин) , Nathan Seiberg, and Brian Willett. Generalized global symmetries. Journal of High Energy Physics, 2015(02):172, February 2015. arXiv:1412.5148, doi:10.1007/JHEP02(2015)172

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep02(2015)172 2015

  5. [5]

    Magnetic monopoles as gauge particles? Physics Letters B, 72(1):117–120, December 1977

    Claus Kalevi Montonen and David Ian Olive. Magnetic monopoles as gauge particles? Physics Letters B, 72(1):117–120, December 1977. doi: 10.1016/0370-2693(77)90076-4

    work page doi:10.1016/0370-2693(77)90076-4 1977

  6. [6]

    Duality transformations of Abelian and non-Abelian gauge fields

    Stanley Deser and Claudio Teitelboim. Duality transformations of Abelian and non-Abelian gauge fields. Physical Review D, 13(6):1592–1597, March

  7. [7]

    doi:10.1103/PhysRevD.13.1592

    work page doi:10.1103/physrevd.13.1592

  8. [8]

    Electric-Magnetic Duality And The Geometric Langlands Program

    Anton Nikolaevich Kapustin (Антон Николаевич Капустин) and Edward Witten. Electric-magnetic duality and the geometric Langlands program. Communications in Number Theory and Physics, 1(1):1–236, January 2007. arXiv:hep-th/0604151, doi:10.4310/CNTP.2007.v1.n1.a1

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.4310/cntp.2007.v1.n1.a1 2007

  9. [9]

    Gauge Theory, Ramification, And The Geometric Langlands Program

    Sergei Gennadievich Gukov (Сергей Геннадьевич Гуков) and Edward Witten. Gauge theory, ramification, and the geometric Langlands program. In David Jerison, Barry Charles Mazur, Tomasz Stanislaw Mrowka, Wilfried Schmid, Richard Peter Stanley, and Shing-Tung Yau (丘成桐), editors, Current Developments in Mathematics 2006, pages 35–180. International Press, Some...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.4310/cdm.2006.v2006.n1.a2 2006

  10. [10]

    Gauge theory and wild ramification

    Edward Witten. Gauge theory and wild ramification. Analysis and Ap- plications, 06(04):429–501, October 2008. arXiv:0710.0631, doi:10.1142/ S0219530508001195

    Pith/arXiv arXiv 2008

  11. [11]

    D-branes, Monopoles and Nahm Equations

    Duiliu-Emanuel Diaconescu. D-branes, monopoles and Nahm equations. Nuclear Physics B, 503(1–2):220–238, October 1997. arXiv:hep-th/9608163, doi:10.1016/S0550-3213(97)00438-0

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0550-3213(97)00438-0 1997

  12. [12]

    Chris D. A. Blair, Johannes Lahnsteiner, Niels Anne Jacob Obers, and Ziqi Yan (燕子骐). Unification of decoupling limits in string and M theory. Physical Review Letters, 132(16):161603, April 2024. arXiv:2311.10564, doi:10.1103/PhysRevLett.132.161603

    work page doi:10.1103/physrevlett.132.161603 2024

  13. [13]

    Non-relativistic M2-branes and the AdS/CFT correspondence

    Neil Lambert and Joseph Smith. Non-relativistic M2-branes and the AdS/CFT correspondence. Journal of High Energy Physics, 2024(06):009, June 2024. arXiv:2401.14955, doi:10.1007/JHEP06(2024)009

    work page doi:10.1007/jhep06(2024)009 2024

  14. [14]

    Chris D. A. Blair, Johannes Lahnsteiner, Niels Anne Jacob Obers, and Ziqi Yan (燕子骐). Matrix theory reloaded: A BPS road to holography. Journal of High Energy Physics, 2025(02):024, February 2025. arXiv:2410.03591, doi:10.1007/JHEP02(2025)024

    work page doi:10.1007/jhep02(2025)024 2025

  15. [15]

    Reciprocal non-relativistic decoupling lim- its of string theory and M-theory

    Neil Lambert and Joseph Smith. Reciprocal non-relativistic decoupling lim- its of string theory and M-theory. Journal of High Energy Physics, 2024(12):094, December 2024. arXiv:2410.17074, doi:10.1007/JHEP12(2024)094. 32

    work page doi:10.1007/jhep12(2024)094 2024

  16. [16]

    Galilean Yang-Mills Theory

    Arjun Bagchi, Rudranil Basu, Ashish Kakkar, and Aditya Mehra. Galilean Yang-Mills theory. Journal of High Energy Physics, 2016(04):051, April 2016. arXiv:1512.08375, doi:10.1007/JHEP04(2016)051

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep04(2016)051 2016

  17. [17]

    Kolekar, and Aditya Mehra

    Arjun Bagchi, Rudranil Basu, Minhajul Islam, Kedar S. Kolekar, and Aditya Mehra. Galilean gauge theories from null reductions. Journal of High Energy Physics, 2022(04):176, April 2022. arXiv:2201.12629, doi: 10.1007/JHEP04(2022)176

    work page doi:10.1007/jhep04(2022)176 2022

  18. [18]

    Constructing Non-Relativistic AdS$_5$/CFT$_4$ Holography

    Andrea Fontanella and Juan Miguel Nieto García. Constructing nonrelativ- istic AdS5/CFT4holography. Physical Review D, 111(2):026003, January 2025. [Erratum: [47]]. arXiv:2403.02379, doi:10.1103/PhysRevD.111.026003

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.111.026003 2025

  19. [19]

    Non-Lorentzian Field Theories with Maximal Supersymmetry and Moduli Space Dynamics

    Neil Lambert and Miles Owen. Non-Lorentzian field theories with maximal supersymmetry and moduli space dynamics. Journal of High Energy Physics, 2018(10):133, October 2018. arXiv:1808.02948, doi: 10.1007/JHEP10(2018)133

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep10(2018)133 2018

  20. [20]

    A remark on the scattering of BPS monopoles

    Nicholas Stephen Manton. A remark on the scattering of BPS monopoles. Physics Letters B, 110(1):54–56, March 1982. doi:10.1016/0370-2693(82) 90950-9

    work page doi:10.1016/0370-2693(82 1982

  21. [21]

    Branched SL(2,ℤ)duality

    Eric Arnold Bergshoeff, Kevin Torres Grosvenor, Johannes Lahnsteiner, Ziqi Yan (燕子骐), and Utku Zorba. Branched SL(2,ℤ)duality. Journal of High Energy Physics, 2022(10):131, October 2022. arXiv:2208.13815, doi:10.1007/JHEP10(2022)131

    work page doi:10.1007/jhep10(2022)131 2022

  22. [22]

    Non-Lorentzian IIB supergravity from a poly- nomial realization of SL(2,ℝ)

    Eric Arnold Bergshoeff, Kevin Torres Grosvenor, Johannes Lahnsteiner, Ziqi Yan (燕子骐), and Utku Zorba. Non-Lorentzian IIB supergravity from a poly- nomial realization of SL(2,ℝ). Journal of High Energy Physics, 2023(12):022, December 2023. arXiv:2306.04741, doi:10.1007/JHEP12(2023)022

    work page doi:10.1007/jhep12(2023)022 2023

  23. [23]

    Anisotropic compactification of nonrelativistic M-theory

    Stephen Ebert and Ziqi Yan (燕子骐). Anisotropic compactification of nonrelativistic M-theory. Journal of High Energy Physics, 2023(11):135, November 2023. arXiv:2309.04912, doi:10.1007/JHEP11(2023)135

    work page doi:10.1007/jhep11(2023)135 2023

  24. [24]

    Chris D. A. Blair, Johannes Lahnsteiner, Niels Anne Jacob Obers, and Ziqi Yan (燕子骐). Dual non-Lorentzian backgrounds for matrix theories. Journal of High Energy Physics, 2025(05):200, May 2025. arXiv:2502.20310, doi:10.1007/JHEP05(2025)200

    work page doi:10.1007/jhep05(2025)200 2025

  25. [25]

    Quantum effects in three-dimensional supersymmetric Galilean Yang-Mills

    Neil Lambert and Joseph Smith. Quantum effects in three-dimensional supersymmetric Galilean Yang-Mills. To be published, 2026

    2026

  26. [26]

    Massive amplitudes on the Coulomb branch of N=4 SYM

    Nathaniel Craig, Henriette Elvang, Michael Kiermaier, and Tracy Slatyer. Massive amplitudes on the Coulomb branch of𝒩 = 4 SYM. Journal of High Energy Physics, 2011(12):097, December 2011. arXiv:1104.2050, doi:10.1007/JHEP12(2011)097

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep12(2011)097 2011

  27. [27]

    An introduction to string Newton-Cartan holography and integrability

    Andrea Fontanella and Juan Miguel Nieto García. An introduction to string Newton-Cartan holography and integrability. Journal of Physics A, 2026. arXiv:2603.24657, doi:10.48550/arXiv.2603.24657. 33

    work page doi:10.48550/arxiv.2603.24657 2026

  28. [28]

    Spin matrix theory: A quantum mechanical model of the AdS/CFT correspondence

    Troels Harmark and Marta Orselli. Spin matrix theory: A quantum mechanical model of the AdS/CFT correspondence. Journal of High Energy Theory, 2014(11):134, November 2014. arXiv:1409.4417, doi:10.1007/ JHEP11(2014)134

    Pith/arXiv arXiv 2014

  29. [29]

    String theory and string Newton–Cartan geometry

    Eric Arnold Bergshoeff, Jaume Gomis, Jan Rosseel, Ceyda Şimşek, and Ziqi Yan (燕子骐). String theory and string Newton–Cartan geometry. Journal of Physics A, 53(1):014001, 2020. arXiv:1907.10668, doi:10.1088/ 1751-8121/ab56e9

    arXiv 2020

  30. [30]

    Torsional string Newton-Cartan geometry for non- relativistic strings

    Leo Bidussi, Troels Harmark, Jelle Hartong, Niels Anne Jacob Obers, and Gerben Oling. Torsional string Newton-Cartan geometry for non- relativistic strings. Journal of High Energy Physics, 2022(02):116, February

    2022

  31. [31]

    arXiv:2107.00642, doi:10.1007/JHEP02(2022)116

    work page doi:10.1007/jhep02(2022)116 2022

  32. [32]

    Grav- itational solitons and non-relativistic string theory

    Troels Harmark, Johannes Lahnsteiner, and Niels Anne Jacob Obers. Grav- itational solitons and non-relativistic string theory. Journal of High En- ergy Physics, 2025(05):199, May 2025. arXiv:2501.10178, doi:10.1007/ JHEP05(2025)199

    arXiv 2025

  33. [33]

    Heterotic string sigma models: Discrete light cone quantization and its current-current deformation

    Eric Arnold Bergshoeff, Kevin Torres Grosvenor, Luca Romano, and Ziqi Yan (燕子骐). Heterotic string sigma models: Discrete light cone quantization and its current-current deformation. Journal of High En- ergy Physics, 2025(09):021, September 2025. arXiv:2505.07458, doi: 10.1007/JHEP09(2025)021

    work page doi:10.1007/jhep09(2025)021 2025

  34. [34]

    Chris D. A. Blair, Domingo Gallegos, and Natale Zinnato. A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry. Journal of High Energy Physics, 2021(10):015, October 2021. arXiv:2104. 07579, doi:10.1007/JHEP10(2021)015

    work page doi:10.1007/jhep10(2021)015 2021

  35. [35]

    Eric Arnold Bergshoeff, Chris D. A. Blair, Johannes Lahnsteiner, and Jan Rosseel. The surprising structure of non-relativistic 11-dimensional supergravity. Journal of High Energy Physics, 2024(12):010, December 2024. arXiv:2407.21648, doi:10.1007/JHEP12(2024)010

    work page doi:10.1007/jhep12(2024)010 2024

  36. [36]

    The M5-brane limit of eleven-dimensional supergravity

    Eric Arnold Bergshoeff, Neil Lambert, and Joseph Smith. The M5-brane limit of eleven-dimensional supergravity. Journal of High Energy Physics, 2025(06):060, June 2025. arXiv:2502.07969, doi:10.1007/JHEP06(2025) 060

    work page doi:10.1007/jhep06(2025 2025

  37. [37]

    Chris D. A. Blair. Supersymmetric solutions of non-relativistic 11- dimensional supergravity. Journal of High Energy Physics, 2025(09):125, September 2025. arXiv:2503.21577, doi:10.1007/JHEP09(2025)125

    work page doi:10.1007/jhep09(2025)125 2025

  38. [38]

    An SL(2,Z) Multiplet of Type IIB Superstrings

    John Henry Schwarz. An 𝑆𝐿(2,ℤ)multiplet of type IIB superstrings. Physics Letters B, 360(1–2):13–18, October 1995. [Erratum: [48]]. arXiv: hep-th/9508143, doi:10.1016/0370-2693(95)01138-G

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/0370-2693(95)01138-g 1995

  39. [39]

    On 𝑆-duality in Abelian gauge theory

    Edward Witten. On 𝑆-duality in Abelian gauge theory. Selecta Math- ematica, 1:383, September 1995. arXiv:hep-th/9505186, doi:10.1007/ BF01671570. 34

    Pith/arXiv arXiv 1995

  40. [40]

    Electromagnetic Duality and Entanglement Anomalies

    William Donnelly, Ben Michel, and Aron Clark Wall. Electromagnetic duality and entanglement anomalies. Physical Review D, 96(4):045008, August 2017. arXiv:1611.05920, doi:10.1103/PhysRevD.96.045008

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.96.045008 2017

  41. [41]

    Duality anomalies in linearized gravity

    Leron Borsten, Michael James Duff, Dimitri Decavel Kanakaris, and Hyung- rok Kim (金炯錄). Duality anomalies in linearized gravity. Physical Review D, 112(4):045010, August 2025. arXiv:2504.15973, doi:10.1103/3nkh-t15m

    work page doi:10.1103/3nkh-t15m 2025

  42. [42]

    TASI Lectures on Solitons

    David Tong. TASI lectures on solitons: Instantons, monopoles, vortices and kinks, September 2005. arXiv:hep-th/0509216, doi:10.48550/arXiv. hep-th/0509216

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv 2005

  43. [43]

    Magnetic Monopole Dynamics, Supersymmetry, and Duality

    Erick James Weinberg and Piljin Yi (ᄋ ᅵ피 ᆯᄌ ᅵᆫ). Magnetic monopole dynamics, supersymmetry, and duality. Physics Reports, 438(2–4):65–236, January 2007. arXiv:hep-th/0609055, doi:10.1016/j.physrep.2006.11.002

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physrep.2006.11.002 2007

  44. [44]

    An exact classical solution for the ’t Hooft monopole and the Julia-Zee dyon

    Manoj Kumar Prasad and Charles Michael Sommerfield. An exact classical solution for the ’t Hooft monopole and the Julia-Zee dyon. Physical Review Letters, 35(12):760–762, September 1975. doi:10.1103/PhysRevLett.35. 760

    work page doi:10.1103/physrevlett.35 1975

  45. [45]

    Dyons of charge 𝑒𝜃/2π

    Edward Witten. Dyons of charge 𝑒𝜃/2π. Physics Letters B, 86(3–4):283–287, October 1979. doi:10.1016/0370-2693(79)90838-4

    work page doi:10.1016/0370-2693(79)90838-4 1979

  46. [46]

    Revisiting the Symmetries of Galilean Electrodynamics

    Andrea Fontanella and Juan Miguel Nieto García. Revisiting the symmetries of Galilean electrodynamics. Journal of High Energy Physics, 2025(06):058, June 2025. arXiv:2411.19217, doi:10.1007/JHEP06(2025)058

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep06(2025)058 2025

  47. [47]

    On Galileian isometries

    Christian Duval. On Galileian isometries. Classical and Quantum Grav- ity, 10(11):2217–2222, November 1993. arXiv:0903.1641, doi:10.1088/ 0264-9381/10/11/006

    Pith/arXiv arXiv 1993

  48. [48]

    Reading between the lines of four-dimensional gauge theories

    Ofer Aharony, Nathan Seiberg, and Yuji Tachikawa (立川裕二). Reading between the lines of four-dimensional gauge theories. Journal of High Energy Physics, 2013(08):115, August 2013. arXiv:1305.0318, doi:10. 1007/JHEP08(2013)115

    arXiv 2013

  49. [49]

    Erratum: Constructing nonrelativistic AdS5/CFT4 holography [Phys

    Andrea Fontanella and Juan Miguel Nieto García. Erratum: Constructing nonrelativistic AdS5/CFT4 holography [Phys. Rev. D 111, 026003 (2025)]. Physical Review D, 112(2):029902, July 2025. doi:10.1103/n1yf-rk6l

    work page doi:10.1103/n1yf-rk6l 2025

  50. [50]

    Erratum: An 𝑆𝐿(2,ℤ)multiplet of type IIB su- perstrings [Phys

    John Henry Schwarz. Erratum: An 𝑆𝐿(2,ℤ)multiplet of type IIB su- perstrings [Phys. Lett. B 360 (1995) 13]. Physics Letters B, 364(4):252–252, December 1995. doi:10.1016/0370-2693(95)01405-5. 35

    work page doi:10.1016/0370-2693(95)01405-5 1995