Pith. sign in

REVIEW 2 major objections 4 minor 62 references

Higgsless Lagrangian SCFTs and Strongly Finite VOAs

T0 review · 2 major / 4 minor · reviewed 2026-07-13 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Higgsless Lagrangian 4d SCFTs are sparse; two of them yield new logarithmic VOAs that are C2-cofinite but non-rational.

desk verdict Two solid new logarithmic VOAs plus a sparse classification of Higgsless Lagrangian SCFTs; the remaining candidates are carefully labelled. read the letter →

arxiv 2607.08813 v1 pith:XGPPUGW5 submitted 2026-07-09 hep-th math-phmath.MPmath.QA

Siqi Chen , Anirudh Deb , Leonardo Rastelli This is my paper · ORCID
classification hep-thmath-phmath.MPmath.QA
keywords vertexoperatoralgebrasstronglyfiniteVOAslogarithmicSCFT/VOAcorrespondenceHiggslessSCFTsC2-cofinitenessHall-Littlewoodindexmodularpseudocharacters
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks which four-dimensional N=2 Lagrangian superconformal theories have no Higgs branch of vacua, because the SCFT/VOA correspondence predicts that such theories produce vertex operator algebras that are strongly finite yet non-rational (logarithmic). Starting from the full Bhardwaj-Tachikawa list of conformal Lagrangians, the authors impose absence of continuous flavor symmetry and then systematically construct gauge-invariant operators that survive F-terms inside subquivers; any theory that admits such an operator is discarded. The survivors form a short list: free vector multiplets and their discrete gaugings, one infinite family of trivalent SO/USp quivers, and three sporadic theories. For two of the sporadics they bootstrap the associated VOAs by writing strong generators, fixing OPEs via Jacobi identities that hold only after null relations are imposed, prove the generators are nilpotent so the associated variety is a point (C2-cofiniteness), and exhibit closed-form vacuum characters whose modular S-transforms contain log-q pseudocharacters, establishing non-rationality. The result both enlarges the sparse catalogue of logarithmic VOAs and supplies concrete new examples whose modular data can be studied in detail.

What carries the argument

The subquiver lemma: a gauge-invariant operator built from half-hypermultiplets of a subquiver that is non-zero modulo the subquiver F-terms remains non-zero in the full theory and, under the geometrization conjecture, is a genuine Higgs-branch generator; this lets whole infinite families be ruled out by inspecting a single recurring pattern.

What would settle it

Compute the full Higgs Hilbert series (or an explicit basis of the F-term quotient ring) for either of the two bootstrapped sporadic theories and find a non-constant generator; or exhibit a modular transformation of their vacuum characters that closes without log-q terms.

Watch

Extended reading notes

Core claim

The complete list of candidate interacting Higgsless Lagrangian SCFTs consists of (i) USp(4) with half-hypers in the 16, (ii) SU(3)×SU(2) with half-hypers in 8×2, (iii) the infinite trivalent USp(m) family for m in 4Z>0, and (iv) the 1/2asym3–USp(8)–SO(6) quiver; the VOAs of (i) and (ii) are C2-cofinite with logarithmic pseudocharacters in the modular orbit of the vacuum character.

Load-bearing premise

The claim that conformal theories have no nilpotent elements in their Higgs chiral ring is used both to turn a single non-vanishing operator into proof of a non-trivial Higgs branch and to read a truncated Hall-Littlewood index as evidence of Higgslessness.

Editorial extensions

If this is right

  • Two previously unknown strongly finite non-rational VOAs, complete with closed-form characters, S and T matrices, and pseudocharacters, become available for representation-category study.
  • Any complete classification of C2-cofinite logarithmic VOAs arising from 4d N=2 SCFTs must at least include the free-vector discrete gaugings, the two sporadic VOAs constructed here, and (conjecturally) the infinite SO/USp family.
  • The modular data of the new VOAs can be used to test proposed Verlinde-type formulae and the structure of log-modular tensor categories.
  • Higgslessness of a Lagrangian SCFT is a practical necessary condition that can be checked by Hilbert-series or HL-index computations before attempting a full VOA bootstrap.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The sparseness of the list suggests that Lagrangian Higgsless theories may be exceptional rather than generic; a unifying geometric or string-theoretic construction of the SO/USp family would explain why the set is so thin.
  • The paper notes that known rational Higgsless SCFTs (Argyres-Douglas) are isolated while the Lagrangian ones have conformal manifolds; this invites a sharp test of whether non-rationality of the VOA is correlated with the existence of exactly marginal couplings.
  • Because the gauginos supply the symplectic-fermion-like degrees of freedom that produce logarithms, any non-Lagrangian Higgsless theory whose VOA is still logarithmic would require a different source of log modules.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper classifies candidate Higgsless Lagrangian 4d N=2 SCFTs within the Bhardwaj–Tachikawa list, concluding that the interacting examples consist of two sporadic theories (USp(4) with half-hypers in the 16; SU(3)×SU(2) with half-hypers in 8×2), one infinite trivalent USp(m) family for m∈4Z>0, and the ½asym3–USp(8)–SO(6) quiver. Free vectors and their discrete gaugings are recovered as the free examples. For the two sporadic theories the authors compute I_Higgs=1, truncate the Hall–Littlewood indices, bootstrap the associated VOAs by OPE ansatz and Jacobi identities (using OPEdefs), exhibit enough null states to prove nilpotency of all strong generators in R_V (hence C2-cofiniteness), and give closed-form vacuum characters whose S-transforms contain logarithmic pseudocharacters, establishing non-rationality. The remaining candidates are left for future VOA constructions, with partial operator-enumeration and HL-truncation evidence.

Significance. Strongly finite non-rational VOAs remain scarce; the two fully constructed algebras are concrete new examples with closed-form characters, explicit S/T matrices, and verified C2-cofiniteness. The classification result is surprising in its sparseness and supplies a short, well-defined list of Lagrangian parents for further logarithmic VOAs. The bootstrap is machine-assisted and checked against independently computed Schur indices; modular non-rationality follows from explicit S-transforms rather than asymptotics alone. These are genuine additions to both the SCFT/VOA dictionary and the mathematical stock of logarithmic VOAs.

major comments (2)
  1. The classification of candidates (Result of §3.1, Table 2) relies on the Higgs-branch geometrization conjecture (C[MH]=RH with no nilpotents) both in the subquiver lemma (§3.3) and in the interpretation of truncated HL indices (§2.5). If nilpotents are allowed, some discarded quivers could still be Higgsless and the subquiver lemma would no longer guarantee a genuine Higgs-branch operator. The paper already labels the infinite family and the third sporadic as candidates with partial evidence; this dependence should be stated more prominently in the Result statement and in the abstract so that the logical status of the full list is unambiguous.
  2. For the infinite family (iii) and the third sporadic (iv), Higgslessness rests on incomplete operator enumeration plus HL truncation for the lowest ranks only (§3.5.3, Eqs. (3.48)–(3.49) and (3.22)). While the authors correctly mark the evidence as non-rigorous, the claim that these are the only remaining candidates would be strengthened by either a complete vanishing argument for a few more ranks or an explicit statement that the list is exhaustive only under the additional assumption that no unexpected higher-dimension singlets appear.
minor comments (4)
  1. In §4.2.1–4.2.2 the schematic forms of the strong generators (Tables 4 and 7) suppress all gauge indices; a short footnote or appendix line indicating the precise contractions would aid reproducibility.
  2. Appendix F lists the null states used for Jacobi identities but does not record the OPEdefs session or the precise order at which the identities were checked; a brief computational note would be useful.
  3. The diagrammatic notation of §3.4 is clear once introduced, but a single worked example of an F-term application (beyond Eq. (3.7)) would help readers less familiar with SO/USp quivers.
  4. Typographical: “Higgslessness” is occasionally hyphenated inconsistently; “pseudocharacters” versus “pseudo-characters” likewise.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: candidate filtering uses an external conjecture, but the two novel VOAs are constructed and verified independently of it.

full rationale

The paper's load-bearing claims for the two sporadic VOAs (USp(4)+16 and SU(3)×SU(2)+8×2) rest on three independent computations that do not reduce to their inputs: (1) direct Macaulay2 evaluation of the Higgs Hilbert series yielding I_Higgs=1 (Secs. 4.2.1–4.2.2), (2) bootstrap of OPEs by imposing Jacobi identities on an ansatz for strong generators, followed by explicit nilpotency of all generators in R_V (Tables 5 and 8), and (3) closed-form vacuum characters whose S-transforms produce logarithmic pseudocharacters (Eqs. 4.27–4.28, 4.42–4.43). These steps match independently computed Schur/Macdonald/HL indices and never invoke the Higgs-branch geometrization conjecture. The Bhardwaj–Tachikawa classification and the SCFT/VOA correspondence are taken as established external input; self-citations are to prior technical tools (indices, free-field realisations, modular asymptotics) that do not force the classification or the VOA properties. The infinite family and third sporadic are carefully labelled candidates whose evidence is partial. No fitted parameter is renamed a prediction, no uniqueness theorem is imported to forbid alternatives, and no ansatz is smuggled that collapses the result to its premises. The derivation is therefore self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central claims rest on the established SCFT/VOA dictionary, the completeness of the Bhardwaj-Tachikawa list of conformal Lagrangian theories, and the Higgs-branch geometrization conjecture that converts ring-theoretic statements into geometric ones. No free parameters are fitted; the two new VOAs are defined by bootstrap rather than by new postulated entities.

assumptions (4)
  • domain assumption Higgs branch geometrization conjecture: for conformal N=2 theories the Higgs chiral ring RH contains no nilpotents and equals the coordinate ring of the Higgs branch.
    Invoked throughout Sections 2.2, 2.5 and 3 to equate RH=C with Higgslessness and to guarantee that a non-vanishing gauge-invariant operator is a genuine Higgs generator.
  • domain assumption Bhardwaj-Tachikawa classification exhausts all 4d N=2 conformal Lagrangian gauge theories.
    The entire case-by-case analysis of Section 3 starts from this list; any missing theory would invalidate completeness of the Higgsless list.
  • domain assumption SCFT/VOA correspondence: the Schur sector of a 4d N=2 SCFT yields a VOA whose associated variety is the Higgs branch (Higgs branch conjecture).
    Used to motivate the search and to interpret C2-cofiniteness of the constructed VOAs as confirmation of the conjecture for the two sporadic cases.
  • standard math Standard facts of vertex-algebra theory (C2 algebra, associated variety, modular linear differential equations, pseudocharacters).
    Background used without proof in Sections 2 and 4.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Higgsless Lagrangian SCFTs and Strongly Finite VOAs." pith.science (2026). https://pith.science/paper/XGPPUGW5

@misc{pith2026260708813,
  author       = {Pith},
  title        = {Pith review of: Higgsless Lagrangian SCFTs and Strongly Finite VOAs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XGPPUGW5}},
  note         = {Machine review of arXiv:2607.08813}
}
abstract

Vertex operator algebras (VOAs) are well studied in both mathematics and physics. The best understood class is that of strongly rational VOAs, whose representation category is maximally well behaved: indeed, it is a modular tensor category. At the next level of complexity are strongly finite but non-rational VOAs. Their representation category is not semisimple (it is ``logarithmic''), but maintains nice structural properties. Only a few families of examples in this class are known, a fact that may have hindered the development of a comprehensive mathematical theory. The SCFT/VOA correspondence provides a natural way to generate more examples: strongly finite but non-rational VOAs are expected to arise from four-dimensional ${\cal N}=2$ Lagrangian superconformal field theories (SCFTs) that do not admit a Higgs branch moduli space of vacua. We tackle the combinatorial task of classifying all such ``Higgsless'' Lagrangian SCFTs. To our surprise, this set turns out to be rather sparse. Free vector multiplets and their discrete gaugings are immediate examples. The interacting Higgsless theories comprise one infinite sequence of SO/USp quivers and three sporadic examples. We construct and study the novel VOAs associated to two of the sporadic examples, and confirm that they are indeed strongly finite and logarithmic.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

62 extracted references · 54 linked inside Pith

  1. [1]

    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), no. 3 1359–1433, [arXiv:1312.5344]

    arXiv 2015

  2. [2]

    Beem and L

    C. Beem and L. Rastelli,Vertex operator algebras, Higgs branches, and modular differential equations, JHEP08(2018) 114, [arXiv:1707.07679]

    arXiv 2018

  3. [3]

    Arakawa,A remark on the C 2-cofiniteness condition on vertex algebras, Math

    T. Arakawa,A remark on the C 2-cofiniteness condition on vertex algebras, Math. Z.270 (2012), no. 1 559–575, [arXiv:1004.1492]

    arXiv 2012

  4. [4]

    Bonetti, C

    F. Bonetti, C. Meneghelli, and L. Rastelli,VOAs labelled by complex reflection groups and 4d SCFTs, JHEP05(2019) 155, [arXiv:1810.03612]

    arXiv 2019

  5. [5]

    C. Beem, C. Meneghelli, and L. Rastelli,Free Field Realizations from the Higgs Branch, JHEP09(2019) 058, [arXiv:1903.07624]

    arXiv 2019

  6. [6]

    C. Beem, C. Meneghelli, W. Peelaers, and L. Rastelli,VOAs and rank-two instanton SCFTs, Commun. Math. Phys.377(2020), no. 3 2553–2578, [arXiv:1907.08629]

    arXiv 2020

  7. [7]

    Beem and C

    C. Beem and C. Meneghelli,Geometric free field realization for the genus-two class S theory of type a1, Phys. Rev. D104(2021), no. 6 065015, [arXiv:2104.11668]

    arXiv 2021

  8. [8]

    C. Beem, A. Deb, M. Martone, C. Meneghelli, and L. Rastelli,Free field realizations for rank-one SCFTs, JHEP12(2024) 004, [arXiv:2407.01674]

    arXiv 2024

Show all 62 references
  1. [9]

    McRae,On rationality forC 2-cofinite vertex operator algebras,arXiv:2108.01898

    R. McRae,On rationality forC 2-cofinite vertex operator algebras,arXiv:2108.01898

  2. [10]

    Miyamoto,Modular invariance of vertex operator algebras satisfying C(2) cofiniteness, math/0209101

    M. Miyamoto,Modular invariance of vertex operator algebras satisfying C(2) cofiniteness, math/0209101

    arXiv

  3. [12]

    Xie and W

    D. Xie and W. Yan,4dN= 2SCFTs and lisse W-algebras, JHEP04(2021) 271, [arXiv:1910.02281]

    2021 arXiv

  4. [13]

    D. Xie, W. Yan, and S.-T. Yau,Chiral algebra of the Argyres-Douglas theory from M5 branes, Phys. Rev. D103(2021), no. 6 065003, [arXiv:1604.02155]

    2021 arXiv

  5. [14]

    Xie and W

    D. Xie and W. Yan,W algebras, cosets and VOAs for 4dN= 2 SCFTs from M5 branes, JHEP04(2021) 076, [arXiv:1902.02838]

    2021 arXiv

  6. [15]

    Xie and W

    D. Xie and W. Yan,Schur sector of Argyres-Douglas theory andW-algebra, SciPost Phys.10 (2021), no. 3 080, [arXiv:1904.09094]

    2021 arXiv

  7. [16]

    Creutzig and A

    T. Creutzig and A. R. Linshaw,Orbifolds of symplectic fermion algebras, Trans. Am. Math. Soc.369(2017), no. 1 467–494, [arXiv:1404.2686]

    2017 arXiv

  8. [17]

    Arabi Ardehali, M

    A. Arabi Ardehali, M. Martone, and M. Rossell´ o,High-temperature expansion of the Schur index and modularity,arXiv:2308.09738

    arXiv

  9. [18]

    Arakawa,Chiral algebras of classSand Moore-Tachikawa symplectic varieties, arXiv:1811.01577

    T. Arakawa,Chiral algebras of classSand Moore-Tachikawa symplectic varieties, arXiv:1811.01577

    arXiv

  10. [19]

    Beem and N

    C. Beem and N. Garner,On the semi-infinite cohomology of graded-unitary vertex algebras, J. Algebra698(2026) 172–223, [arXiv:2509.10364]

    2026 arXiv

  11. [20]

    Bhardwaj and Y

    L. Bhardwaj and Y. Tachikawa,Classification of 4d N=2 gauge theories, JHEP12(2013) 100, [arXiv:1309.5160]. – 54 –

    2013 arXiv

  12. [21]

    F. A. Dolan and H. Osborn,On short and semi-short representations for four-dimensional superconformal symmetry, Annals Phys.307(2003) 41–89, [hep-th/0209056]

    2003 arXiv

  13. [22]

    Gadde, L

    A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan,The 4d Superconformal Index from q-deformed 2d Yang-Mills, Phys. Rev. Lett.106(2011) 241602, [arXiv:1104.3850]

    2011 arXiv

  14. [23]

    Gadde, L

    A. Gadde, L. Rastelli, S. S. Razamat, and W. Yan,Gauge Theories and Macdonald Polynomials, Commun. Math. Phys.319(2013) 147–193, [arXiv:1110.3740]

    2013 arXiv

  15. [24]

    M. A. Luty and W. Taylor,Varieties of vacua in classical supersymmetric gauge theories, Phys. Rev. D53(1996) 3399–3405, [hep-th/9506098]

    1996 arXiv

  16. [25]

    C. Beem, M. Lemos, P. Liendo, L. Rastelli, and B. C. van Rees,TheN= 2superconformal bootstrap, JHEP03(2016) 183, [arXiv:1412.7541]

    2016 arXiv

  17. [26]

    Zhu, Vertex operator algebras, elliptic functions and modular forms

    Y. Zhu, Vertex operator algebras, elliptic functions and modular forms. Yale University, 1990

    1990

  18. [27]

    P. C. Argyres and M. R. Douglas,New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B448(1995) 93–126, [hep-th/9505062]

    1995 arXiv

  19. [28]

    Xie,General Argyres-Douglas Theory, JHEP01(2013) 100, [arXiv:1204.2270]

    D. Xie,General Argyres-Douglas Theory, JHEP01(2013) 100, [arXiv:1204.2270]

    2013 arXiv

  20. [29]

    Creutzig and D

    T. Creutzig and D. Ridout,Logarithmic Conformal Field Theory: Beyond an Introduction, J. Phys. A46(2013) 4006, [arXiv:1303.0847]

    2013 arXiv

  21. [30]

    Adamovic and A

    D. Adamovic and A. Milas,C 2-cofiniteW-algebras and their logarithmic representations, arXiv:1212.6771

    arXiv

  22. [31]

    Di Pietro and Z

    L. Di Pietro and Z. Komargodski,Cardy formulae for SUSY theories ind=4 andd=6, JHEP12(2014) 031, [arXiv:1407.6061]

    2014 arXiv

  23. [32]

    Buican and T

    M. Buican and T. Nishinaka,On the superconformal index of Argyres–Douglas theories, J. Phys. A49(2016), no. 1 015401, [arXiv:1505.05884]

    2016 arXiv

  24. [33]

    Arabi Ardehali,High-temperature asymptotics of supersymmetric partition functions, JHEP07(2016) 025, [arXiv:1512.03376]

    A. Arabi Ardehali,High-temperature asymptotics of supersymmetric partition functions, JHEP07(2016) 025, [arXiv:1512.03376]

    2016 arXiv

  25. [34]

    Arakawa and K

    T. Arakawa and K. Kawasetsu,Quasi-lisse vertex algebras and modular linear differential equations,arXiv:1610.05865

    arXiv

  26. [35]

    N. J. Hitchin, A. Karlhede, U. Lindstrom, and M. Rocek,Hyperkahler Metrics and Supersymmetry, Commun. Math. Phys.108(1987) 535

    1987

  27. [36]

    Rastelli and B

    L. Rastelli and B. C. Rayhaun,Rationality in four dimensions, Phys. Rev. D109(2024), no. 10 105018, [arXiv:2308.06312]

    2024 arXiv

  28. [37]

    Macaulay2, a software system for research in algebraic geometry

    D. R. Grayson and M. E. Stillman, “Macaulay2, a software system for research in algebraic geometry.” Available athttps://macaulay2.com/

  29. [38]

    Gaiotto,N=2 dualities, JHEP08(2012) 034, [arXiv:0904.2715]

    D. Gaiotto,N=2 dualities, JHEP08(2012) 034, [arXiv:0904.2715]

    2012 arXiv

  30. [39]

    Gaiotto, G

    D. Gaiotto, G. W. Moore, and A. Neitzke,Wall-crossing, Hitchin systems, and the WKB approximation, Adv. Math.234(2013) 239–403, [arXiv:0907.3987]

    2013 arXiv

  31. [40]

    Hanany and N

    A. Hanany and N. Mekareeya,Tri-vertices and SU(2)’s, JHEP02(2011) 069, [arXiv:1012.2119]

    2011 arXiv

  32. [41]

    Thielemans, An Algorithmic approach to operator product expansions, W algebras and W strings

    K. Thielemans, An Algorithmic approach to operator product expansions, W algebras and W strings. PhD thesis, Leuven U., 1994.hep-th/9506159. – 55 –

    1994 arXiv

  33. [42]

    H. G. Kausch,Symplectic fermions, Nucl. Phys. B583(2000) 513–541, [hep-th/0003029]

    2000 arXiv

  34. [43]

    Creutzig and T

    T. Creutzig and T. Gannon,Logarithmic conformal field theory, log-modular tensor categories and modular forms, J. Phys. A50(2017), no. 40 404004, [arXiv:1605.04630]

    2017 arXiv

  35. [44]

    S. D. Mathur, S. Mukhi, and A. Sen,On the Classification of Rational Conformal Field Theories, Phys. Lett. B213(1988) 303–308

    1988

  36. [45]

    M. R. Gaberdiel and H. G. Kausch,A Rational logarithmic conformal field theory, Phys. Lett. B386(1996) 131–137, [hep-th/9606050]

    1996 arXiv

  37. [46]

    M. R. Gaberdiel,An Algebraic approach to logarithmic conformal field theory, Int. J. Mod. Phys. A18(2003) 4593–4638, [hep-th/0111260]

    2003 arXiv

  38. [47]

    Flohr and M

    M. Flohr and M. R. Gaberdiel,Logarithmic torus amplitudes, J. Phys. A39(2006) 1955–1968, [hep-th/0509075]

    2006 arXiv

  39. [48]

    M. R. Gaberdiel and I. Runkel,The Logarithmic triplet theory with boundary, J. Phys. A39 (2006) 14745–14780, [hep-th/0608184]

    2006 arXiv

  40. [49]

    Miyamoto,C 2-cofiniteness of cyclic-orbifold models, Communications in Mathematical Physics335(2015), no

    M. Miyamoto,C 2-cofiniteness of cyclic-orbifold models, Communications in Mathematical Physics335(2015), no. 3 1279–1286

    2015

  41. [50]

    A. B. Zamolodchikov,Infinite Additional Symmetries in Two-Dimensional Conformal Quantum Field Theory, Theor. Math. Phys.65(1985) 1205–1213

    1985

  42. [51]

    Bouwknegt and K

    P. Bouwknegt and K. Schoutens,W symmetry in conformal field theory, Phys. Rept.223 (1993) 183–276, [hep-th/9210010]

    1993 arXiv

  43. [52]

    Blumenhagen, M

    R. Blumenhagen, M. Flohr, A. Kliem, W. Nahm, A. Recknagel, and R. Varnhagen,W algebras with two and three generators, Nucl. Phys. B361(1991) 255–289

    1991

  44. [53]

    Beem and H

    C. Beem and H. Kulkarni,Towards a classification of graded unitaryW 3 algebras, arXiv:2602.15944

    arXiv

  45. [54]

    Arabi Ardehali, C

    A. Arabi Ardehali, C. Beem, M. Lemos, and L. Rastelli,Graded unitarity in the SCFT/VOA correspondence,JHEP06(2026) 075, [arXiv:2507.23781]

    2026 arXiv

  46. [55]

    Argyres, M

    P. Argyres, M. Lotito, Y. L¨ u, and M. Martone,Geometric constraints on the space ofN= 2 SCFTs. Part I: physical constraints on relevant deformations, JHEP02(2018) 001, [arXiv:1505.04814]

    2018 arXiv

  47. [56]

    P. C. Argyres, M. Lotito, Y. L¨ u, and M. Martone,Geometric constraints on the space ofN = 2 SCFTs. Part II: construction of special K¨ ahler geometries and RG flows, JHEP02 (2018) 002, [arXiv:1601.00011]

    2018 arXiv

  48. [57]

    Argyres, M

    P. Argyres, M. Lotito, Y. L¨ u, and M. Martone,Geometric constraints on the space ofN= 2 SCFTs. Part III: enhanced Coulomb branches and central charges, JHEP02(2018) 003, [arXiv:1609.04404]

    2018 arXiv

  49. [58]

    P. C. Argyres, M. Lotito, Y. L¨ u, and M. Martone,Expanding the landscape ofN= 2 rank 1 SCFTs, JHEP05(2016) 088, [arXiv:1602.02764]

    2016 arXiv

  50. [59]

    Argyres and M

    P. Argyres and M. Martone,Construction and classification of Coulomb branch geometries, arXiv:2003.04954

    2003 arXiv

  51. [60]

    A. Deb, C. Meneghelli, and L. Rastelli,The Nilpotency Index for 4dN= 2SCFTs, arXiv:2503.05975. – 56 –

    arXiv

  52. [61]

    Romelsberger,Counting chiral primaries in N = 1, d=4 superconformal field theories, Nucl

    C. Romelsberger,Counting chiral primaries in N = 1, d=4 superconformal field theories, Nucl. Phys. B747(2006) 329–353, [hep-th/0510060]

    2006 arXiv

  53. [62]

    Kinney, J

    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]

    2007 arXiv

  54. [63]

    F. A. Dolan and H. Osborn,Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories, Nucl. Phys. B818(2009) 137–178, [arXiv:0801.4947]. – 57 –

    2009 arXiv

Pith tools

Reviewed July 13, 2026 · model on record in the stance chip above.