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arxiv: 2512.23603 · v3 · pith:NFNY2HOBnew · submitted 2025-12-29 · ✦ hep-th

Two roads to fortuity in ABJM theory

Connor Behan , Leonardo Pipolo de Gioia This is my paper

Pith reviewed 2026-05-21 16:43 UTC · model grok-4.3

classification ✦ hep-th
keywords fortuitous operatorsABJM theorynilpotent superchargeBMN subsectorcentralizer algebrasupersymmetric gauge theoryChern-Simons matterweak coupling
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The pith

Fortuitous operators in ABJM theory are enumerated at low levels and matched to an infinite tower from N=4 SYM via truncation.

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

The paper explores fortuitous operators in weakly coupled ABJM theory using two approaches. First, it adapts an algorithm from N=4 SYM to list 244 low-lying examples and group them by the centralizer algebra, yielding explicit representatives that are leading at N=3 but subleading at N=2. Second, it finds a truncation of ABJM where the one-loop supercharge behaves exactly as in the BMN subsector of N=4 SYM. This match lets an entire known tower of such operators be carried over from one theory to the other. A sympathetic reader would care because these operators are tied to the holographic description of extremal black holes, and finding them systematically helps test the dictionary at finite N.

Core claim

By adapting the nilpotent supercharge cohomology algorithm, 244 low-lying fortuitous operators are enumerated in ABJM and sorted into multiplets of the centralizer algebra, producing two leading representatives for N=3. Separately, a truncation is identified in which the one-loop supercharge action coincides with that in the BMN subsector of N=4 SYM, permitting the lift of a known infinite tower of representatives.

What carries the argument

The cohomology of a nilpotent supercharge, which isolates the fortuitous operators, combined with a truncation of the ABJM action that replicates the one-loop supercharge of the BMN subsector.

Load-bearing premise

That the chosen truncation of ABJM theory makes the one-loop supercharge action identical to the BMN subsector without additional terms or loss of the required supersymmetry properties.

What would settle it

An explicit computation of the two-loop contribution to the supercharge in the truncated ABJM model that fails to match the corresponding term in the N=4 SYM BMN subsector would disprove the exact matching.

Figures

Figures reproduced from arXiv: 2512.23603 by Connor Behan, Leonardo Pipolo de Gioia.

Figure 1
Figure 1. Figure 1: Distribution of file sizes in the search for the simplest fortuitous cohomology class [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
read the original abstract

A recently proposed addition to the holographic dictionary connects extremal black holes to fortuitous operators -- those which are only supersymmetric for sufficiently small values of the central charge. The most efficient techniques for finding them come from studying the cohomology of a nilpotent supercharge. We explore two aspects of this problem in weakly-coupled ABJM theory, where the gauge group is $\mathrm{U}(N) \times \mathrm{U}(N)$ and the Chern-Simons level is taken to be large. Adapting an algorithm which has been used to great effect in $\mathcal{N} = 4$ Super Yang-Mills, we enumerate 244 low-lying fortuitous operators and sort them into multiplets of the centralizer algebra. This leads to the construction of two leading fortuitous representatives for $N = 3$ which are subleading for $N = 2$. In the second part of this work, we identify a truncation of ABJM theory where the action of the one-loop supercharge matches the one in the BMN subsector of $\mathcal{N} = 4$ Super Yang-Mills. This allows a known infinite tower of representatives to be lifted from one theory to the other.

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

2 major / 2 minor

Summary. The manuscript adapts an algorithm from N=4 SYM to enumerate 244 low-lying fortuitous operators in weakly-coupled ABJM theory (U(N)×U(N) gauge group, large Chern-Simons level). These are sorted into multiplets of the centralizer algebra, yielding two explicit leading fortuitous representatives for N=3 (subleading for N=2). In the second part, a truncation of ABJM is identified in which the one-loop supercharge acts identically to its counterpart in the BMN subsector of N=4 SYM, permitting an infinite tower of representatives to be lifted between the theories.

Significance. If the truncation matching holds without extra corrections, the work supplies a concrete dictionary bridge between fortuitous operators in ABJM and N=4 SYM, directly relevant to the holographic description of extremal black holes. The algorithmic enumeration of 244 operators is a clear strength, providing a substantial, in-principle reproducible dataset and explicit constructions for small N.

major comments (2)
  1. [§4] §4 (truncation identification): the central claim that the one-loop supercharge Q_1 acts identically to the BMN case rests on the truncation killing all additional diagrams. No explicit verification is given that Chern-Simons vertices or bifundamental matter loops vanish inside the chosen sector; if any survive, the nilpotent cohomology and lifted tower receive corrections absent from N=4 SYM.
  2. [Enumeration section] Enumeration and multiplet sorting (around the 244-operator list): while the algorithm is adapted from prior N=4 SYM work, the manuscript does not supply a representative table or explicit centralizer-algebra action for the two constructed N=3 leading representatives, making it difficult to assess how the sorting supports the subleading-for-N=2 claim.
minor comments (2)
  1. Notation for the centralizer algebra and the precise definition of the truncation (e.g., which fields and interactions are retained) could be stated more explicitly in the introductory paragraphs of the second part to aid readability.
  2. The abstract states the gauge group as U(N)×U(N) but does not repeat the large-k limit when summarizing the truncation; a single clarifying sentence would remove ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major points below and will revise the manuscript to incorporate additional explicit material as suggested.

read point-by-point responses

  1. Referee: [§4] §4 (truncation identification): the central claim that the one-loop supercharge Q_1 acts identically to the BMN case rests on the truncation killing all additional diagrams. No explicit verification is given that Chern-Simons vertices or bifundamental matter loops vanish inside the chosen sector; if any survive, the nilpotent cohomology and lifted tower receive corrections absent from N=4 SYM.

    Authors: We thank the referee for highlighting this point. The truncation is defined by restricting to a specific set of operators whose quantum numbers ensure that only diagrams common to the BMN sector contribute at one loop. Nevertheless, we agree that an explicit check of the vanishing of Chern-Simons vertices and bifundamental matter loops would strengthen the claim. In the revised version we will add a dedicated paragraph (or short appendix) that computes the relevant diagrams inside the truncated sector and confirms their cancellation, thereby establishing that the one-loop supercharge matches the BMN case without extra corrections. revision: yes

  2. Referee: [Enumeration section] Enumeration and multiplet sorting (around the 244-operator list): while the algorithm is adapted from prior N=4 SYM work, the manuscript does not supply a representative table or explicit centralizer-algebra action for the two constructed N=3 leading representatives, making it difficult to assess how the sorting supports the subleading-for-N=2 claim.

    Authors: We agree that explicit examples would make the multiplet structure and the N=3 versus N=2 distinction easier to verify. In the revised manuscript we will include a new table that lists the two leading fortuitous representatives for N=3, together with their explicit action under the centralizer algebra generators. This will directly illustrate how the sorting into multiplets is performed and why the same operators become subleading for N=2. revision: yes

Circularity Check

0 steps flagged

Derivation relies on independent algorithmic enumeration and explicit truncation matching

full rationale

The paper adapts a known algorithm from N=4 SYM to enumerate 244 operators in ABJM and performs an explicit identification of a truncation where the one-loop supercharge action matches the BMN subsector. These steps are presented as direct computations rather than reductions to fitted parameters or self-referential definitions. No load-bearing self-citations, ansatze smuggled via prior work, or predictions that equal their inputs by construction are evident in the provided derivation outline. The central claims rest on external algorithmic reuse and sector-specific matching, both of which are falsifiable by independent verification outside the paper's own data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract alone, no explicit free parameters, axioms, or invented entities are detailed beyond standard assumptions in weakly-coupled ABJM at large Chern-Simons level and the definition of fortuitous operators from the holographic dictionary.

pith-pipeline@v0.9.0 · 5740 in / 1304 out tokens · 35947 ms · 2026-05-21T16:43:28.858817+00:00 · methodology

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supports
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Forward citations

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Reference graph

Works this paper leans on

68 extracted references · 68 canonical work pages · cited by 4 Pith papers · 30 internal anchors

  1. [1]

    Snowmass White Paper: Micro- and Macro-Structure of Black Holes,

    I. Bena, E. J. Martinec, S. D. Mathur, and N. P. Warner, “Snowmass White Paper: Micro- and Macro-Structure of Black Holes,”arXiv:2203.04981 [hep-th]

    work page arXiv

  2. [2]

    Microscopic Origin of the Bekenstein-Hawking Entropy

    A. Strominger and C. Vafa, “Microscopic Origin of the Bekenstein-Hawking Entropy,” Phys. Lett. B379(1996) 99–104,arXiv:hep-th/9601029 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  3. [3]

    The Large N Limit of Superconformal Field Theories and Supergravity

    J. Maldacena, “The Large N Limit of Superconformal Field Theories and Supergravity,” Int. J. Theor. Phys.38(1999) 231–252,arXiv:hep-th/9711200 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  4. [4]

    Supersymmetric AdS5 black holes

    J. B. Gutowski and H. S. Reall, “Supersymmetric AdS5 black holes,”JHEP02(2004) 006,arXiv:hep-th/0401042 [hep-th]. 38

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  5. [5]

    General supersymmetric AdS5 black holes

    J. B. Gutowski and H. S. Reall, “General supersymmetric AdS5 black holes,”JHEP04 (2004) 048,arXiv:hep-th/0401129 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  6. [6]

    An Index for 4 dimensional Super Conformal Theories

    J. Kinney, J. M. Maldacena, S. Minwalla, and S. Raju, “An index for 4 dimensional super conformal theories,”Commun. Math. Phys.275(2007) 209–254,hep-th/0510251

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  7. [7]

    An extremization principle for the entropy of rotating BPS black holes in AdS$_5$

    S. M. Hosseini, K. Hristov, and A. Zaffaroni, “An extremization principle for the entropy of rotating BPS black holes in AdS 5,”JHEP07(2017) 106,arXiv:1705.05383 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  8. [8]

    Microscopic origin of the Bekenstein-Hawking entropy of supersymmetricAdS 5 black holes,

    A. Cabo-Bizet, D. Cassani, D. Martelli, and S. Murthy, “Microscopic origin of the Bekenstein-Hawking entropy of supersymmetricAdS 5 black holes,”JHEP10(2019) 062, arXiv:1810.11442 [hep-th]

    work page arXiv 2019

  9. [9]

    Large AdS black holes from QFT,

    S. Choi, J. Kim, S. Kim, and J. Nahmgoong, “Large AdS black holes from QFT,” arXiv:1810.12067 [hep-th]

    work page arXiv

  10. [10]

    Black holes in 4dN= 4 Super Yang-Mills from field theory,

    F. Benini and E. Milan, “Black holes in 4dN= 4 Super Yang-Mills from field theory,” Phys. Rev. X10(2020) 021037,arXiv:1812.09613 [hep-th]

    work page arXiv 2020

  11. [11]

    N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals

    O. Aharony, O. Bergman, D. L. Jafferis, and J. Maldacena, “N= 6 superconformal Chern-Simons matter theories, M2 branes and their gravity duals,”JHEP10(2008) 091, arXiv:0806.1218 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  12. [12]

    Black hole microstates in AdS$_4$ from supersymmetric localization

    F. Benini, K. Hristov, and A. Zaffaroni, “Black hole microstates in AdS 4 from supersymmetric localization,”JHEP05(2016) 054,arXiv:1511.04085 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  13. [13]

    Exact microstate counting for dyonic black holes in AdS4,

    F. Benini, K. Hristov, and A. Zaffaroni, “Exact microstate counting for dyonic black holes in AdS4,”Phys. Lett. B771(2017) 462–466,arXiv:1608.07294 [hep-th]

    work page arXiv 2017

  14. [14]

    Comments on 1/16 BPS Quantum States and Classical Configurations

    L. Grant, P. A. Grassi, S. Kim, and S. Minwalla, “Comments on 1/16 BPS Quantum States and Classical Configurations,”JHEP05(2008) 049,arXiv:0803.4183 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  15. [15]

    1/16 BPS States in N=4 SYM

    C.-M. Chang and X. Yin, “1/16 BPS States inN= 4 SYM,”Phys. Rev. D88(2013) 1006005,arXiv:1305.6314 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  16. [16]

    Words to describe a black hole,

    C.-M. Chang and Y.-H. Lin, “Words to describe a black hole,”JHEP02(2023) 109, arXiv:2209.06728 [hep-th]

    work page arXiv 2023

  17. [17]

    The shape of non-graviton operators forSU(2),

    S. Choi, S. Kim, E. Lee, and J. Park, “The shape of non-graviton operators forSU(2),” arXiv:2209.12696 [hep-th]

    work page arXiv

  18. [18]

    Following black hole states,

    K. Budzik, H. Murali, and P. Vieira, “Following black hole states,”arXiv:2306.04693 [hep-th]. 39

    work page arXiv

  19. [19]

    Holographic covering and the fortuity of black holes,

    C.-M. Chang and Y.-H. Lin, “Holographic covering and the fortuity of black holes,” arXiv:2402.10129 [hep-th]

    work page arXiv

  20. [20]

    Bosonic Fortuity in Vector Models,

    R. de Mello Koch, A. Ghosh, and H. J. R. Van Zyl, “Bosonic Fortuity in Vector Models,” JHEP06(2025) 246,arXiv:2504.14181 [hep-th]

    work page arXiv 2025

  21. [21]

    Fortuity with a single matrix,

    Y. Chen, “Fortuity with a single matrix,”arXiv:2511.00790 [hep-th]

    work page arXiv

  22. [22]

    Fortuity in SYK Models,

    C.-M. Chang, Y. Chen, B. S. Sia, and Z. Yang, “Fortuity in SYK Models,”JHEP08 (2025) 003,arXiv:2412.06902 [hep-th]

    work page arXiv 2025

  23. [23]

    Fortuity in the D1-D5 system,

    C.-M. Chang, Y.-H. Lin, and H. Zhang, “Fortuity in the D1-D5 system,” arXiv:2501.05448 [hep-th]

    work page arXiv

  24. [24]

    Fortuity and supergravity,

    M. R. R. Hughes and M. Shigemori, “Fortuity and supergravity,”arXiv:2505.14888 [hep-th]

    work page arXiv

  25. [25]

    Fortuity and R-charge concentration in the D1-D5 CFT,

    C.-M. Chang and H. Zhang, “Fortuity and R-charge concentration in the D1-D5 CFT,” arXiv:2511.23294 [hep-th]

    work page arXiv

  26. [26]

    Fortuity and relevant deformation,

    J. Choi and S. Kim, “Fortuity and relevant deformation,”arXiv:2512.12764 [hep-th]

    work page arXiv

  27. [27]

    Fractional M2-branes

    O. Aharony, O. Bergman, and D. L. Jafferis, “Fractional M2-branes,”JHEP11(2008) 043,arXiv:0807.4924 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  28. [28]

    BPS phases and fortuity in higher spin holography,

    S. Kim, J. Lee, S. Lee, and H. Oh, “BPS phases and fortuity in higher spin holography,” arXiv:2511.03105 [hep-th]

    work page arXiv

  29. [29]

    Fortuity in ABJM,

    A. Belin, P. Singh, R. Vadala, and A. Zaffaroni, “Fortuity in ABJM,”arXiv:2512.04146 [hep-th]

    work page arXiv

  30. [30]

    Violation of S-duality in classicalQ-cohomology,

    C.-M. Chang and Y.-H. Lin, “Violation of S-duality in classicalQ-cohomology,” arXiv:2510.24008 [hep-th]

    work page arXiv

  31. [31]

    Konishi lifts a black hole,

    J. Choi and E. Lee, “Konishi lifts a black hole,”arXiv:2511.09519 [hep-th]

    work page arXiv

  32. [32]

    Loop Corrected Supercharges from Holomorphic Anomalies,

    K. Budzik and J. Kulp, “Loop Corrected Supercharges from Holomorphic Anomalies,” arXiv:2512.07771 [hep-th]

    work page arXiv

  33. [33]

    Towards quantum black hole microstates,

    S. Choi, S. Kim, E. Lee, S. Lee, and J. Park, “Towards quantum black hole microstates,” JHEP11(2023) 175,arXiv:2304.10155 [hep-th]

    work page arXiv 2023

  34. [34]

    ABJ Triality: from Higher Spin Fields to Strings

    C.-M. Chang, S. Minwalla, T. Sharma, and X. Yin, “ABJ Triality: from Higher Spin Fields to Strings,”J. Phys. A. Math. Theor.46(2013) 214009,arXiv:1207.4485 [hep-th]. 40

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  35. [35]

    ABJ Correlators with Weakly Broken Higher Spin Symmetry,

    D. J. Binder, S. M. Chester, and M. Jerdee, “ABJ Correlators with Weakly Broken Higher Spin Symmetry,”JHEP04(2021) 242,arXiv:2103.01969 [hep-th]

    work page arXiv 2021

  36. [36]

    Semi-Chiral Operators in 4dN= 1 Gauge Theories,

    K. Budzik, D. Gaiotto, J. Kulp, B. R. Williams, J. Wu, and M. Yu, “Semi-Chiral Operators in 4dN= 1 Gauge Theories,”JHEP05(2024) 245,arXiv:2306.01039 [hep-th]

    work page arXiv 2024

  37. [37]

    Supergravitons from one loop perturbative N=4 SYM

    R. A. Janik and M. Trzetrzelewski, “Supergravitons from one loop perturbativeN= 4 SYM,”Phys. Rev. D77(2008) 085024,arXiv:0712.2714 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  38. [38]

    N=5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds

    K. Hosomichi, K.-M. Lee, S. Lee, S. Lee, and J. Park, “N= 5,6 Superconformal Chern-Simons Theories and M2-branes on Orbifolds,”JHEP09(2008) 002, arXiv:0806.4977 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  39. [39]

    Supersymmetry enhancement by monopole operators

    D. Bashkirov and A. Kapustin, “Supersymmetry enhancement by monopole operators,” JHEP05(2011) 015,arXiv:1007.4861 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  40. [40]

    Monopole operators and symmetry enhancement in ABJM theory revisited,

    S. Hu, “Monopole operators and symmetry enhancement in ABJM theory revisited,” Phys. Rev. D104(2021) 125018,arXiv:2110.01335 [hep-th]

    work page arXiv 2021

  41. [41]

    ABJ Quadrality

    M. Honda, Y. Pang, and Y. Zhu, “ABJ Quadrality,”JHEP11(2017) 190, arXiv:1708.08472 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  42. [42]

    Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory

    D. Gaiotto and E. Witten, “Janus Configurations, Chern-Simons Couplings, And The Theta-Angle inN= 4 Super Yang-Mills Theory,”JHEP06(2010) 097,arXiv:0804.2907 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  43. [43]

    Multiplets of Superconformal Symmetry in Diverse Dimensions

    C. Cordova, T. T. Dumitrescu, and K. Intriligator, “Multiplets of superconformal symmetry in diverse dimensions,”arXiv:1612.00809 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  44. [44]

    The complete superconformal index for N=6 Chern-Simons theory

    S. Kim, “The complete superconformal index forN= 6 Chern-Simons theory,”Nucl. Phys. B821(2009) 241–284,arXiv:0903.4172 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  45. [45]

    On Superconformal Characters and Partition Functions in Three Dimensions

    F. A. Dolan, “On superconformal characters and partition functions in three dimensions,” arXiv:0811.2740 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  46. [46]

    Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry

    M. A. Bandres, A. E. Lipstein, and J. H. Schwarz, “Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry,”JHEP09(2008) 027,arXiv:0807.0880 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  47. [47]

    Decoding stringy near-supersymmetric black holes,

    C.-M. Chang, L. Feng, Y.-H. Lin, and Y.-X. Tao, “Decoding stringy near-supersymmetric black holes,”SciPost Physics16(2024) 109,arXiv:2306.04673 [hep-th]. 41

    work page arXiv 2024

  48. [48]

    Probing non-graviton spectra inN= 4 SYM via BMN truncation and S-duality,

    A. Gadde, E. Lee, R. Raj, and S. Tomar, “Probing non-graviton spectra inN= 4 SYM via BMN truncation and S-duality,”arXiv:2506.13887 [hep-th]

    work page arXiv

  49. [49]

    FiniteNblack hole cohomologies,

    J. Choi, S. Choi, S. Kim, J. Lee, and S. Lee, “FiniteNblack hole cohomologies,”JHEP 12(2024) 029,arXiv:2312.16443 [hep-th]

    work page arXiv 2024

  50. [50]

    Brane-fused black hole operators,

    R. de Mello Koch, M. Kim, S. Kim, J. Lee, and S. Lee, “Brane-fused black hole operators,”JHEP07(2025) 216,arXiv:2412.08695 [hep-th]

    work page arXiv 2025

  51. [51]

    To gauge or to double gauge? Matrix models, global symmetry, and black hole cohomologies,

    A. Gaikwad, T. Kibe, S. van Leuven, and K. Mathieson, “To gauge or to double gauge? Matrix models, global symmetry, and black hole cohomologies,”2512.02103

    work page arXiv

  52. [52]

    Bonus Symmetries of N=4 Super-Yang-Mills Correlation Functions via AdS Duality

    K. Intriligator, “Bonus Symmetries ofN= 4 Super Yang-Mills correlation functions via AdS duality,”Nucl. Phys. B551(1999) 575–600,arXiv:hep-th/9811047 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  53. [53]

    Bonus Symmetry and the Operator Product Expansion of N=4 Super-Yang-Mills

    K. Intriligator and W. Skiba, “Bonus Symmetry and the Operator Product Expansion of N= 4 Super Yang-Mills,”Nucl. Phys. B559(1999) 165–183,arXiv:hep-th/9905020 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  54. [54]

    The ${\cal N} = 8$ Superconformal Bootstrap in Three Dimensions

    S. M. Chester, J. Lee, S. S. Pufu, and R. Yacoby, “TheN= 8 superconformal bootstrap in three dimensions,”JHEP09(2014) 143,arXiv:1406.4814 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  55. [55]

    Gluon Scattering in AdS from CFT,

    L. F. Alday, C. Behan, P. Ferrero, and X. Zhou, “Gluon Scattering in AdS from CFT,” JHEP06(2021) 020,arXiv:2103.15830 [hep-th]

    work page arXiv 2021

  56. [56]

    Notes on Superconformal Representations in Two Dimensions,

    S. Lee and S. Lee, “Notes on Superconformal Representations in Two Dimensions,”Nucl. Phys. B956(2020) 115033,arXiv:1911.10391 [hep-th]

    work page arXiv 2020

  57. [57]

    Plane-wave Matrix Theory from N=4 Super Yang-Mills on RxS^3

    N. Kim, T. Klose, and J. Plefka, “Plane-wave Matrix Theory fromN= 4 Super Yang-Mills onR×S 3,”Nucl. Phys. B671(2003) 359–382,arXiv:hep-th/0306054 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  58. [58]

    Strings in flat space and pp waves from ${\cal N}=4$ Super Yang Mills

    D. Berenstein, J. Maldacena, and H. Nastase, “Strings in flat space and pp waves from N= 4 Super Yang Mills,”JHEP04(2002) 013,arXiv:hep-th/0202021 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  59. [59]

    Field redefinition rules for auxiliary field searches,

    V. O. Rivelles and J. G. Taylor, “Field redefinition rules for auxiliary field searches,”J. Phys. A. Math. Gen.15(1982) 2819

    work page 1982

  60. [60]

    Off-shell no-go theorems for higher dimensional supersymmetries and supergravities,

    V. O. Rivelles and J. G. Taylor, “Off-shell no-go theorems for higher dimensional supersymmetries and supergravities,”Phys. Lett. B121(1983) 37–41

    work page 1983

  61. [61]

    Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory

    T. Bargheer, F. Loebbert, and C. Meneghelli, “Symmetries of Tree-level Scattering Amplitudes inN= 6 Superconformal Chern-Simons Theory,”Phys. Rev. D82(2010) 045016,arXiv:1003.6120 [hep-th]. 42

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  62. [62]

    BPS and near-BPS black holes inAdS 5 and their spectrum inN=4SYM,

    J. Boruch, M. Heydeman, L. V. Iliesiu, and G. J. Turiaci, “BPS and near-BPS black holes inAdS 5 and their spectrum inN=4SYM,”JHEP07(2025) 220,arXiv:2203.01331 [hep-th]

    work page arXiv 2025

  63. [63]

    The spectrum of near-BPS Kerr-Newman black holes and the ABJM mass gap,

    M. Heydeman and C. Toldo, “The spectrum of near-BPS Kerr-Newman black holes and the ABJM mass gap,”JHEP06(2025) 177,arXiv:2412.03697 [hep-th]

    work page arXiv 2025

  64. [64]

    The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability

    N. Beisert, “The Dilatation Operator ofN= 4 Super Yang-Mills Theory and Integrability,”Phys. Rept.405(2004) 1–202,arXiv:hep-th/0407277 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  65. [65]

    Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory

    B. I. Zwiebel, “Two-loop Integrability of PlanarN= 6 Superconformal Chern-Simons Theory,”J. Phys. A: Math. Theor.42(2009) 495402,arXiv:0901.0411 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  66. [66]

    Infinite Chiral Symmetry in Four Dimensions

    C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli, and B. C. van Rees, “Infinite Chiral Symmetry in Four Dimensions,”Commun. Math. Phys.336(2015) 1359–1433, arXiv:1312.5344 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  67. [67]

    On 1 8-BPS black holes and the chiral algebra of N= 4 SYM,

    C.-M. Chang, Y.-H. Lin, and J. Wu, “On 1 8-BPS black holes and the chiral algebra of N= 4 SYM,”Adv. Theor. Math. Phys.28(2024) 2431–2489,arXiv:2310.20086 [hep-th]

    work page arXiv 2024

  68. [68]

    The 3dN= 6 bootstrap: From higher spins to strings to membranes,

    D. J. Binder, S. M. Chester, M. Jerdee, and S. S. Pufu, “The 3dN= 6 bootstrap: From higher spins to strings to membranes,”JHEP05(2021) 083,arXiv:2011.05728 [hep-th]. 43

    work page arXiv 2021