Pith. sign in

REVIEW 3 major objections 6 minor 2 cited by

Generalized Schur partition functions and RG flows

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The generalized Schur partition function of SU(2) N_f=4 SQCD, evaluated at alpha = h^vee_g / 6, reproduces the Schur indices of every SCFT in the Deligne-Cvitanovic rank-one series.

desk verdict A transparent, suggestive conjecture paper that maps the Deligne-Cvitanovic rank-one series into a one-parameter deformation of the SU(2) N_f=4 Schur index, with the higher-rank extension still genuinely conjectural. read the letter →

arxiv 2506.13764 v2 pith:DZPZBF4X submitted 2025-06-16 hep-th math-phmath.MP

Anirudh Deb , Shlomo S. Razamat This is my paper
classification hep-thmath-phmath.MP
keywords alphapartitionfunctionindexschurscftscertaindeformations
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 Schur index is a way of counting protected operators in a 4d N=2 superconformal field theory. The authors define a one-parameter deformation of this index, written as Z(q,alpha), by taking a special double-scaling limit of the full superconformal index. Setting alpha=1 gives the ordinary Schur index. Setting alpha=0 gives a trivial answer associated with free photons on a singular locus of the Coulomb branch. The limit interpolates between these two extreme ways of ordering the limits.

The main observation is that for specific values of alpha, the q-series of this deformed index is exactly the ordinary Schur index of a different SCFT. In particular, starting from the SU(2) gauge theory with four flavors, the values alpha = 1/5, 1/3, 1/2, 2, 3, 5 give the Schur indices of the a0, a1, a2 Argyres-Douglas theories and the e6, e7, e8 Minahan-Nemeschansky theories. The general rule is alpha = h^vee_g / 6, where h^vee_g is the dual Coxeter number of the flavor symmetry algebra.

The authors extend this pattern to higher rank gauge theories and propose a conjecture: two SCFTs on different corners of a Coulomb branch have related generalized Schur partition functions, with alpha mapping between them, provided their central charges and Coulomb branch dimensions obey certain relations. The evidence comes from comparing the first few terms in q expansions; no complete derivation is given.

Extended reading notes

Core claim

The central claim is that the normalized generalized Schur partition function is invariant under certain mass and vev deformations: two SCFTs on different corners of the same Coulomb branch have the same partition function with a nontrivial parameter map, Z_1(q, alpha_1) = Z_2(q, alpha_2(alpha_1)). In particular, the Schur indices of all SCFTs in the Deligne-Cvitanovic series are obtained from the SU(2) N_f=4 SQCD expression by setting alpha = h^vee_g / 6 (Eq. 11 and Table I).

Load-bearing premise

The relation between Coulomb branch scaling dimensions in the proposed higher-rank conjecture, Delta_i^(2) = (Delta_i^(1) - 1) alpha + 1 (Eq. 13), is called an 'experimental' observation by the authors and has no derivation. This relation is used to identify which pairs of theories can have partition functions related by the alpha-map, so if it fails for some pair, the conjecture as stated would be false.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper defines a double-scaled limit of the N=2 superconformal index, producing a partition function \hat Z(q, α) that interpolates between the Schur index at α=1 and the Coulomb-branch-trivialized index at α=0. The main claim is that for pairs of SCFTs connected by certain mass/vev deformations on the Coulomb branch, these partition functions coincide with a nontrivial parameter map, \hat Z_1(q, α_1) = \hat Z_2(q, α_2(α_1)). For the rank-one example of SU(2) N_f=4 SQCD, the paper observes that at α = h^∨_g/6 the function reproduces the Schur indices (or VOA vacuum characters) of the Deligne-Cvitanović series. A higher-rank generalization is proposed in which a necessary condition for such an equality is that central charges and Coulomb-branch scaling dimensions transform as in Eq. (13). The evidence consists of explicit series expansions for integer α to high order and for fractional α to low order, plus tables of series for SU(N) and USp(2N) SQCD.

Significance. The rank-one observation, if correct, is a striking and elegant result: it encodes the entire Deligne-Cvitanović family of Schur indices as special values of a single one-parameter partition function, and it makes a falsifiable prediction for the e8 case beyond the Macdonald index. The paper is transparent about the evidence: the integer-α checks are extensive, and the fractional-α checks are low-order but align with known results. The higher-rank conjecture is more speculative: Eq. (13) is explicitly 'experimental' and unproved, and the checks in Tables II and III are sparse and low-order for fractional α. Nonetheless, the paper presents a clear framework and concrete testable predictions, which is valuable even while the conjecture remains open. The use of independently known Schur indices as checks avoids circularity.

major comments (3)
  1. [Higher rank and other generalizations] The higher-rank conjecture as stated in Eqs. (12)–(13) rests on the Coulomb-branch scaling-dimension relation Δ_i^{(2)} = (Δ_i^{(1)} - 1) α + 1, which the paper itself labels 'experimental' and for which no derivation is given. This relation is load-bearing because it is the selection criterion used to generate the pairs in Tables II and III; without a derivation or a clean test that distinguishes prediction from fitting, the conjecture remains a guess. In particular, the paper does not provide a higher-rank example with fractional α verified beyond low orders in q, nor does it demonstrate that a pair satisfying the central-charge relation but not the scaling-dimension relation fails to satisfy Eq. (12). I recommend either deriving Eq. (13) from Coulomb branch geometry or adding at least one nontrivial higher-rank test (e.g., a case not already contained in the infinite series of Tables II and III) with the equality verified to higher order in q.
  2. [Case study of rank1, Eq. (10) and Table I] For fractional values of α (1/5, 1/3, 1/2, 3/2, 2/3, etc.), the identification with the Deligne-Cvitanović Schur indices is verified only to low orders in q (e.g., up to q^3 in Eq. (10)) by numerical contour integration. Since the equality is claimed for all orders, the paper should state the maximal q-order to which each fractional-α row of Table I has been checked, and ideally extend the checks using the modular linear differential equations satisfied by the target Schur indices [19]. The integer-α cases (α = 2,3,5) are checked to higher orders and are convincing, but the fractional cases are the novel part of the rank-one claim and need more support.
  3. [Higher rank and other generalizations, text below Eq. (13)] The paper states that Eq. (13) gives a 'necessary condition' for Eq. (12), but the subsequent discussion and tables treat the condition as effectively sufficient: the pairs in Tables II and III are selected by saturating these relations, and no counterexample is discussed. Please clarify whether the conjecture is that these conditions are sufficient (at least within the class of theories considered), or merely necessary and observed to hold in examples. This distinction is essential for the interpretation of the higher-rank claim.
minor comments (6)
  1. [Higher rank and other generalizations, footnote 8] The sentence 'We have made sporadic checks of this statement' about the MLDE order matching is vague; please specify which theories and to what order in q the checks were performed.
  2. [Introduction and generalized Schur partition functions] The text says 'we allow for any non-negative real value of α' in footnote 3 but later uses 'For general α ∈ R+' in the main text; please clarify whether α=0 is included and explicitly state the behavior of the normalized partition function at α=0.
  3. [TQFT structure of Z(q, α), Eq. (16)] The expression for ψ0(a) is given with an expansion up to q^3 but without a definition of the normalization convention beyond ψ0(1)=1; please state the defining integral or recurrence used to produce this wave-function.
  4. [References] Reference [55] is listed as 'T. Dumitrescu, G. Festuccia, M. Del Zotto, Talk at NatiFest 2016' with no title or preprint number; please provide a complete citation or remove it.
  5. [Case study of rank1, paragraph after Eq. (10)] The sentence 'The entries a0, a1, a2, e6, e7, e8 in the Deligne-Cvitanović series are special cases of tables II and III' should make the identification explicit by stating the relevant values of N for each row of Tables II and III.
  6. [Summary and Discussion] The statements about the (A3,A3) AD theory and the (A2,D4) AD theory being obtained by diagonal gauging are asserted without an explicit computation; please provide a reference or an outline of the index computation supporting these claims.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the generalized Schur identities are checked against independently known indices; the unproved scaling-dimension relation is a conjecture, not a circular fit.

full rationale

The paper's central equality Z_1(q, alpha_1) = Z_2(q, alpha_2(alpha_1)) is not built into the definition of the partition function. The generalized limit is defined in Eqs. (4)-(7) as a specialization of the full index, with alpha=1 giving the Schur index; the special values alpha = h^vee/6 in Table I are tied to dual Coxeter numbers, and the resulting q-series are compared with known Schur indices of Argyres-Douglas and Minahan-Nemeschansky theories (Eq. (10)). These are independent external benchmarks, so no fitted-input-called-prediction pattern appears. The higher-rank proposal in Eqs. (12)-(13) contains a genuinely conjectural element: the Coulomb-branch scaling-dimension relation Delta_i^(2) = (Delta_i^(1)-1) alpha + 1 is explicitly called an 'experimental' observation and is not derived. This is a load-bearing assumption and a correctness risk, but it is not circular: the partition functions involved are computed independently, and the failure mode would be falsity of the conjecture, not equivalence to its inputs. The paper itself flags this gap in the Summary: 'It will be extremely interesting to find a first principle derivation of the experimental observations.' The few self-citations (e.g., [18], [47], [63]) appear as background tools and are not the sole support for the main claim; no uniqueness theorem is imported to force the choice of alpha. Overall, no significant circularity; the score reflects only minor non-load-bearing self-citations.

Assumptions & free parameters 1 free parameters · 4 assumptions · 1 invented entities

The main free ingredient is the continuous parameter alpha. The axioms are standard physics background plus the assumption that low-order q-expansion matches suffice. No new particles or forces are introduced.

free parameters (1)
  • alpha = special values h^vee_g/6 for Deligne series entries; otherwise arbitrary real
    The continuous parameter defining the generalized Schur limit. The special values are chosen according to the dual Coxeter number, not fitted to the q-series coefficients.
assumptions (4)
  • domain assumption The double-scaling limit in Eq. (4) is well-defined for all alpha in R+ after stripping poles and dividing by N(alpha).
    Needed for the normalized partition function to be finite and for its q-expansion to exist. The paper checks this only in examples.
  • domain assumption Equality of the first few q-expansion coefficients with known Schur indices implies equality of the full series.
    Used throughout the paper to identify Z(q,alpha) with the Schur index of another SCFT; fractional alpha checks extend only to low orders.
  • domain assumption The superconformal index is invariant under S-duality and standard RG-flow manipulations, following Refs. [18,52,53].
    The paper relies on this background principle when arguing that related theories have related partition functions.
  • domain assumption The Shapere-Tachikawa central charge relation applies to the conjectural theories appearing in the alpha-map.
    Used to derive the transformation of the a central charge from the c and dimension relations.
invented entities (1)
  • Generalized Schur partition function Z(q,alpha) independent evidence
    purpose: Interpolates between the Schur index (alpha=1) and the Coulomb-branch pole limit (alpha=0), and at special alpha values reproduces Schur indices of other SCFTs.
    The object is explicitly defined by Eq. (7), reduces to the known Schur index at alpha=1, and reproduces known SCFT indices at special values up to checked orders.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Generalized Schur partition functions and RG flows." pith.science (2026). https://pith.science/paper/DZPZBF4X

@misc{pith2026250613764,
  author       = {Pith},
  title        = {Pith review of: Generalized Schur partition functions and RG flows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DZPZBF4X}},
  note         = {Machine review of arXiv:2506.13764}
}
abstract

We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,\alpha)$, has a standard $q$-expansion with coefficients depending on a continuous parameter $\alpha$. The Schur index is a special case with $\alpha=1$. Through explicit computations we argue that this partition function is an invariant of certain mass deformations and vacuum expectation value (vev) deformations of the SCFT. In particular, two SCFTs residing in different corners of the same Coulomb branch, satisfying certain restrictive conditions, have the same partition function with a non-trivial map of the parameters, $\hat {\cal Z}_1(q,\alpha_1)=\hat {\cal Z}_2(q,\alpha_2(\alpha_1))$. For example, we show that the Schur index of all the SCFTs in the Deligne-Cvitanovi\'c series is given by special values of $\alpha$ of the partition function of the SU(2) $N_f=4$ ${\cal N}=2$ SQCD.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

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

  1. Argyres-Douglas Theories, Macdonald Indices and Arc Space of Zhu Algebra

    hep-th 2025-07 conditional novelty 7.0 of 10

    The MacDonald index of (A1, D_{2n+1}) Argyres-Douglas theories is conjectured to be a closed q,t product-sum, and the refined character of a strongly finitely generated VOA is proven to equal the arc-space Hilbert ser...

  2. Supersymmetric zeta functions and determinants

    hep-th 2025-11 conditional novelty 6.0 of 10

    Residues and special values of supersymmetric zeta functions (built from single-particle indices) are conjectured to reproduce anomaly coefficients, Casimir energies, and central charges across 2d/4d/6d.

Reference graph

Works this paper leans on

64 extracted references · 17 canonical work pages · cited by 2 Pith papers

  1. [19]

    Vertex operator algebras, Higgs branches, and modular differential equations,

    C. Beem, L. Rastelli, “Vertex operator algebras, Higgs branches, and modular differential equations,” JHEP 08, 114 (2018) [arXiv:1707.07679 [hep-th]]

    arXiv 2018

  2. [1]

    The 4d Superconformal Index from q-deformed 2d Yang–Mills,

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

    arXiv 2011

  3. [2]

    Gauge Theories and Macdonald Polynomials,

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

    arXiv 2013

  4. [3]

    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, 209-254 (2007) [arXiv:hep- th/0510251 [hep-th]]

    arXiv 2007

  5. [4]

    Infinite Chiral Symmetry in Four Di- mensions,

    C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli, B. C. van Rees, “Infinite Chiral Symmetry in Four Di- mensions,” Commun. Math. Phys. 336, no.3, 1359-1433 (2015) [arXiv:1312.5344 [hep-th]]

    arXiv 2015

  6. [5]

    Infrared Compu- tations of Defect Schur Indices,

    C. Cordova, D. Gaiotto, S. H. Shao, “Infrared Compu- tations of Defect Schur Indices,” JHEP 11, 106 (2016) [arXiv:1606.08429 [hep-th]]

    arXiv 2016

  7. [6]

    SYK-Schur duality: Dou- ble scaled SYK correlators from N = 2 supersymmetric gauge theory,

    D. Gaiotto and H. Verlinde, “SYK-Schur duality: Dou- ble scaled SYK correlators from N = 2 supersymmetric gauge theory,” [arXiv:2409.11551 [hep-th]]

    arXiv

  8. [7]

    Schur Quantization and Complex Chern-Simons theory,

    D. Gaiotto and J. Teschner, “Schur Quantization and Complex Chern-Simons theory,” [arXiv:2406.09171 [hep- th]]

    arXiv

Show all 64 references
  1. [8]

    Renormalization Group flow in Schur quantization,

    F. Ambrosino and D. Gaiotto, “Renormalization Group flow in Schur quantization,” [arXiv:2503.16685 [hep-th]]

    arXiv

  2. [9]

    3D TFTs from 4d N = 2 BPS particles,

    D. Gaiotto and H. Kim, “3D TFTs from 4d N = 2 BPS particles,” JHEP 03, 173 (2025) [arXiv:2409.20393 [hep- th]]

    2025 arXiv

  3. [10]

    Cordova and S

    C. Cordova and S. H. Shao, ‘Schur Indices, BPS Particles, and Argyres-Douglas Theories,” JHEP 01, 040 (2016) [arXiv:1506.00265 [hep-th]]

    2016 arXiv

  4. [11]

    Nee- dles in a haystack. An algorithmic approach to the clas- sification of 4d N = 2 SCFTs,

    J. Kaidi, M. Martone, L. Rastelli and M. Weaver, “Nee- dles in a haystack. An algorithmic approach to the clas- sification of 4d N = 2 SCFTs,” JHEP 03, 210 (2022) [arXiv:2202.06959 [hep-th]]

    2022 arXiv

  5. [12]

    Coulomb Branch Operator Algebras and Universal Selection Rules for N = 2 SCFTs,

    M. Buican, “Coulomb Branch Operator Algebras and Universal Selection Rules for N = 2 SCFTs,” [arXiv:2406.00178 [hep-th]]

    arXiv

  6. [13]

    Argyres- Douglas Theories, Chiral Algebras and Wild Hitchin Characters,

    L. Fredrickson, D. Pei, W. Yan and K. Ye, “Argyres- Douglas Theories, Chiral Algebras and Wild Hitchin Characters,” JHEP 01, 150 (2018) [arXiv:1701.08782 [hep-th]]

    2018 arXiv

  7. [14]

    Mirror symmetry for circle com- pactified 4d A1 class-S theories,

    Y. Pan and W. Yan, “Mirror symmetry for circle com- pactified 4d A1 class-S theories,” [arXiv:2410.15695 [hep- th]]

    arXiv

  8. [15]

    The Nilpotency Index for 4d N = 2 SCFTs,

    A. Deb, C. Meneghelli and L. Rastelli, “The Nilpotency Index for 4d N = 2 SCFTs,” [arXiv:2503.05975 [hep-th]]

    arXiv

  9. [16]

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

    C. Romelsberger, “Counting chiral primaries in N = 1, d=4 superconformal field theories,” Nucl. Phys. B 747, 329-353 (2006) [arXiv:hep-th/0510060 [hep-th]]

    2006 arXiv

  10. [17]

    Applications of the Su- perconformal Index for Protected Operators and q- Hypergeometric Identities to N=1 Dual Theories,

    F. A. Dolan and H. Osborn, “Applications of the Su- perconformal Index for Protected Operators and q- Hypergeometric Identities to N=1 Dual Theories,” Nucl. Phys. B 818, 137-178 (2009) [arXiv:0801.4947 [hep-th]]

    2009 arXiv

  11. [18]

    Bootstrap- ping the superconformal index with surface defects,

    D. Gaiotto, L. Rastelli and S. S. Razamat, “Bootstrap- ping the superconformal index with surface defects,” JHEP 01, 022 (2013) [arXiv:1207.3577 [hep-th]]. 6

    2013 arXiv

  12. [20]

    Supercon- formal Index, BPS Monodromy and Chiral Algebras,

    S. Cecotti, J. Song, C. Vafa and W. Yan, “Supercon- formal Index, BPS Monodromy and Chiral Algebras,” JHEP 11, 013 (2017) [arXiv:1511.01516 [hep-th]]

    2017 arXiv

  13. [21]

    R-Twisting and 4d/2d Correspondences,

    S. Cecotti, A. Neitzke and C. Vafa, “R-Twisting and 4d/2d Correspondences,” [arXiv:1006.3435 [hep-th]]

    arXiv

  14. [22]

    A Family of Vertex Operator Al- gebras from Argyres-Douglas Theory,

    H. Kim and J. Song, “A Family of Vertex Operator Al- gebras from Argyres-Douglas Theory,” [arXiv:2412.20015 [hep-th]]

  15. [23]

    S- duality and 2d Topological QFT,

    A. Gadde, E. Pomoni, L. Rastelli, S. S. Razamat, “ S- duality and 2d Topological QFT,” JHEP 03, 032 (2010) [arXiv:0910.2225 [hep-th]]

    2010 arXiv

  16. [24]

    Down the rabbit hole with theories of class S,

    S. S. Razamat and B. Willett, “Down the rabbit hole with theories of class S,” JHEP 10, 099 (2014) [arXiv:1403.6107 [hep-th]]

    2014 arXiv

  17. [25]

    3d dualities from 4d dualities,

    O. Aharony, S. S. Razamat, N. Seiberg and B. Willett, “3d dualities from 4d dualities,” JHEP 07, 149 (2013) [arXiv:1305.3924 [hep-th]]

    2013 arXiv

  18. [26]

    New phenomena in SU(3) supersymmetric gauge theory,

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

    1995 arXiv

  19. [27]

    New N=2 superconformal field theories in four- dimensions,

    P. C. Argyres, M. R. Plesser, N. Seiberg and E. Wit- ten, “New N=2 superconformal field theories in four- dimensions,” Nucl. Phys. B461, 71-84 (1996) [arXiv:hep- th/9511154 [hep-th]]

    1996

  20. [28]

    An N=2 super- conformal fixed point with E(6) global symmetry,

    J. A. Minahan and D. Nemeschansky, “An N=2 super- conformal fixed point with E(6) global symmetry,” Nucl. Phys. B 482, 142-152 (1996) [arXiv:hep-th/9608047 [hep- th]]

    1996 arXiv

  21. [29]

    Superconformal fixed points with E(n) global symmetry,

    J. A. Minahan and D. Nemeschansky, “Superconformal fixed points with E(n) global symmetry,” Nucl. Phys. B 489, 24-46 (1997) [arXiv:hep-th/9610076 [hep-th]]

    1997 arXiv

  22. [30]

    Geo- metric constraints on the space of N = 2 SCFTs. Part I: physical constraints on relevant deformations,

    P. Argyres, M. Lotito, Y. L¨ u and M. Martone, “Geo- metric constraints on the space of N = 2 SCFTs. Part I: physical constraints on relevant deformations,” JHEP 02, 001 (2018) [arXiv:1505.04814 [hep-th]]

    2018 arXiv

  23. [31]

    Geo- metric constraints on the space of N = 2 SCFTs. Part II: construction of special K¨ ahler geometries and RG flows,

    P. C. Argyres, M. Lotito, Y. L¨ u and M. Martone, “Geo- metric constraints on the space of N = 2 SCFTs. Part II: construction of special K¨ ahler geometries and RG flows,” JHEP 02, 002 (2018) [arXiv:1601.00011 [hep-th]]

    2018 arXiv

  24. [32]

    Geomet- ric constraints on the space of N = 2 SCFTs. Part III: enhanced Coulomb branches and central charges,

    P. Argyres, M. Lotito, Y. L¨ u and M. Martone, “Geomet- ric constraints on the space of N = 2 SCFTs. Part III: enhanced Coulomb branches and central charges,” JHEP 02, 003 (2018) [arXiv:1609.04404 [hep-th]]

    2018 arXiv

  25. [33]

    Construction and classifica- tion of Coulomb branch geometries,

    P. Argyres and M. Martone, “Construction and classifica- tion of Coulomb branch geometries,” [arXiv:2003.04954 [hep-th]]

    2003 arXiv

  26. [34]

    Quasi-lisse vertex al- gebras and modular linear differential equations,

    T. Arakawa, K. Kawasetsu, “Quasi-lisse vertex al- gebras and modular linear differential equations,” [arXiv:1610.05865 [math.QA]]

    arXiv

  27. [35]

    On intermediate Lie al- gebra E7+1/2,

    K. Lee, K. Sun and H. Wang, “On intermediate Lie al- gebra E7+1/2,” Lett. Math. Phys. 114, no.1, 13 (2024) [arXiv:2306.09230 [math-ph]]

    2024 arXiv

  28. [36]

    experimental

    (see also [37, 38]). More- over, [38] describe an N = 1 Lagrangian which flows in the IR to an N = 2 theory, with central charges, Coulomb branch di- branch RG flows. Let us comment that for α > 1 we obtain theories which can be deformed on their Coulomb branch to flow to the ...

  29. [37]

    Computational evidence for deligne’s conjecture regarding exceptional lie groups

    Arjeh M Cohen and Ronald de Man. Computational evidence for deligne’s conjecture regarding exceptional lie groups. Comptes Rendus de l’Acad´ emie des Sciences. S´ erie 1. Math´ ematique, 322(5):427–432, 1996

    1996

  30. [38]

    Looking for the G 2 Higgs branch of 4D rank 1 SCFTs,

    M. Abhishek, S. Grover, D. P. Jatkar and K. Singh, “Looking for the G 2 Higgs branch of 4D rank 1 SCFTs,” JHEP 08, 026 (2024) [arXiv:2312.00275 [hep-th]]

    2024 arXiv

  31. [39]

    Large landscape of 4d superconformal field theories from small gauge theories,

    M. Cho, K. Maruyoshi, E. Nardoni and J. Song, “Large landscape of 4d superconformal field theories from small gauge theories,” JHEP 11, 010 (2024) [arXiv:2408.02953 [hep-th]]

    2024 arXiv

  32. [40]

    Magnetic quivers for rank 1 theories,

    A. Bourget, J. F. Grimminger, A. Hanany, M. Sperling, G. Zafrir and Z. Zhong, “Magnetic quivers for rank 1 theories,” JHEP 09, 189 (2020) [arXiv:2006.16994 [hep- th]]

    2020 arXiv

  33. [41]

    Enhancement of Supersym- metry via Renormalization Group Flow and the Super- conformal Index,

    K. Maruyoshi and J. Song, “Enhancement of Supersym- metry via Renormalization Group Flow and the Super- conformal Index,” Phys. Rev. Lett. 118, no.15, 151602 (2017) [arXiv:1606.05632 [hep-th]]

    2017 arXiv

  34. [42]

    N = 1 deformations and RG flows of N = 2 SCFTs,

    K. Maruyoshi and J. Song, “ N = 1 deformations and RG flows of N = 2 SCFTs,” JHEP 02, 075 (2017) [arXiv:1607.04281 [hep-th]]

    2017 arXiv

  35. [43]

    Cardy formulae for SUSY theories in d = 4 and d = 6,

    L. Di Pietro and Z. Komargodski, “Cardy formulae for SUSY theories in d = 4 and d = 6,” JHEP 12, 031 (2014) [arXiv:1407.6061 [hep-th]]

    2014 arXiv

  36. [44]

    High-temperature asymptotics of su- persymmetric partition functions,

    A. Arabi Ardehali, “High-temperature asymptotics of su- persymmetric partition functions,” JHEP 07, 025 (2016) [arXiv:1512.03376 [hep-th]]

    2016 arXiv

  37. [45]

    On the superconformal index of Argyres–Douglas theories,

    M. Buican and T. Nishinaka, “On the superconformal index of Argyres–Douglas theories,” J. Phys. A 49, no.1, 015401 (2016) [arXiv:1505.05884 [hep-th]]

    2016 arXiv

  38. [46]

    High- temperature expansion of the Schur index and modular- ity,

    A. Arabi Ardehali, M. Martone and M. Rossell´ o, “High- temperature expansion of the Schur index and modular- ity,” [arXiv:2308.09738 [hep-th]]

    arXiv

  39. [47]

    Supersym- metric Casimir Energy and the Anomaly Polynomial,

    N. Bobev, M. Bullimore and H. C. Kim, “Supersym- metric Casimir Energy and the Anomaly Polynomial,” JHEP 09, 142 (2015) doi:10.1007/JHEP09(2015)142 [arXiv:1507.08553 [hep-th]]

    2015 arXiv

  40. [48]

    On a modular property of N=2 super- conformal theories in four dimensions,

    S. S. Razamat, “On a modular property of N=2 super- conformal theories in four dimensions,” JHEP 10, 191 (2012) [arXiv:1208.5056 [hep-th]]

    2012 arXiv

  41. [49]

    Central charges of N=2 superconformal field theories in four dimensions,

    A. D. Shapere and Y. Tachikawa, “Central charges of N=2 superconformal field theories in four dimensions,” JHEP 09, 109 (2008) [arXiv:0804.1957 [hep-th]]

    2008 arXiv

  42. [50]

    N =1 De- formations and RG flows of N =2 SCFTs, part II: non-principal deformations,

    P. Agarwal, K. Maruyoshi and J. Song, “ N =1 De- formations and RG flows of N =2 SCFTs, part II: non-principal deformations,” JHEP 12, 103 (2016) [arXiv:1610.05311 [hep-th]]

    2016 arXiv

  43. [51]

    Testing our understanding of SCFTs: a catalogue of rank-2 N = 2 theories in four dimensions,

    M. Martone, “Testing our understanding of SCFTs: a catalogue of rank-2 N = 2 theories in four dimensions,” JHEP 07, 123 (2022) [arXiv:2102.02443 [hep-th]]

    2022 arXiv

  44. [52]

    On the compactification of 5d theories to 4d,

    M. Martone and G. Zafrir, “On the compactification of 5d theories to 4d,” JHEP 08, 017 (2021) [arXiv:2106.00686 [hep-th]]

    2021 arXiv

  45. [53]

    Rigid Supersymmetric Theories in Curved Superspace,

    G. Festuccia and N. Seiberg, “Rigid Supersymmetric Theories in Curved Superspace,” JHEP 06, 114 (2011) [arXiv:1105.0689 [hep-th]]

    2011 arXiv

  46. [54]

    The supersymmetric in- dex in four dimensions,

    L. Rastelli and S. S. Razamat, “The supersymmetric in- dex in four dimensions,” J. Phys. A 50, no.44, 443013 (2017) [arXiv:1608.02965 [hep-th]]

    2017 arXiv

  47. [55]

    The Exact supercon- formal R symmetry maximizes a,

    K. A. Intriligator and B. Wecht, “The Exact supercon- formal R symmetry maximizes a,” Nucl. Phys. B 667, 183-200 (2003) [arXiv:hep-th/0304128 [hep-th]]

    2003 arXiv

  48. [56]

    Dumitrescu, G

    T. Dumitrescu, G. Festuccia, M. Del Zotto, Talk at Nat- iFest 2016

    2016

  49. [57]

    On the chiral algebra of Argyres-Douglas theories and S-duality,

    J. Choi and T. Nishinaka, “On the chiral algebra of Argyres-Douglas theories and S-duality,” JHEP 04, 004 (2018) [arXiv:1711.07941 [hep-th]]

    2018 arXiv

  50. [58]

    Infinitely many 4D N=2 SCFTs with a=c and beyond,

    M. J. Kang, C. Lawrie and J. Song, “Infinitely many 4D N=2 SCFTs with a=c and beyond,” Phys. Rev. D 104, no.10, 105005 (2021) [arXiv:2106.12579 [hep-th]]

    2021 arXiv

  51. [59]

    N =1 La- grangians for generalized Argyres-Douglas theories,

    P. Agarwal, A. Sciarappa and J. Song, “ N =1 La- grangians for generalized Argyres-Douglas theories,” 7 JHEP 10, 211 (2017) [arXiv:1707.04751 [hep-th]]

    2017 arXiv

  52. [60]

    N = 2 dualities,

    D. Gaiotto, “ N = 2 dualities,” JHEP 08, 034 (2012) [arXiv:0904.2715 [hep-th]]

    2012 arXiv

  53. [61]

    Four- dimensional wall-crossing via three-dimensional field theory,

    D. Gaiotto, G. W. Moore and A. Neitzke, “Four- dimensional wall-crossing via three-dimensional field theory,” Commun. Math. Phys. 299, 163-224 (2010) [arXiv:0807.4723 [hep-th]]

    2010 arXiv

  54. [62]

    An elliptic hypergeometric integral with W (F4) symmetry,

    F. J. van de Bult, “An elliptic hypergeometric integral with W (F4) symmetry,”, Ramanujan J. 25 (2011), no. 1, 1–20 [arXiv:0909.4793[math]]

    2011 arXiv

  55. [63]

    Q-operators for the Ruijse- naars model,

    E. Rains and H. Rosengren, “Q-operators for the Ruijse- naars model,” [arXiv:2503.18057 [math-ph]]

    arXiv

  56. [64]

    Ground state wavefunctions of elliptic relativistic integrable Hamiltonians,

    B. Nazzal, A. Nedelin and S. S. Razamat, “Ground state wavefunctions of elliptic relativistic integrable Hamiltonians,” Nucl. Phys. B 996, 116364 (2023) [arXiv:2305.09718 [hep-th]]

    2023 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.