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REVIEW 2 major objections 4 minor 68 references

Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper determines, uniquely and dimension-independently, the superconformal blocks that appear in four-point functions of mixed half-BPS operators in SCFTs with SU(2) R-symmetry.

desk verdict Solid technical extension of superconformal block technology to mixed half-BPS correlators; the all-orders completeness claim is the main thing to press on in review. read the letter →

arxiv 1908.02768 v2 pith:UTIYFL6E submitted 2019-08-07 hep-th

Florent Baume , Michael Fuchs , Craig Lawrie This is my paper · ORCID
classification hep-th PACS 11.25.Hf11.30.Pb
keywords superconformalblockshalf-BPSoperatorsSU(2)R-symmetryconformalbootstrapWardidentityCasimirequationJackpolynomialssix-dimensionalSCFT
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

This paper works out the explicit superconformal blocks for the four-point function of four different half-BPS superconformal primaries—operators annihilated by half of the supercharges—in any superconformal field theory with SU(2) R-symmetry, for spacetime dimensions 2

What carries the argument

The central object is the decomposition Gχ(u,v;w)=ΣJ,m,n PJ(w) fJΔ+m,ℓ+n gΔ12,Δ34Δ+m,ℓ+n(u,v), where PJ(w) are the SU(2)R harmonics, g are the bosonic conformal blocks, and the coefficients f carry the superconformal multiplet structure. The argument runs by expanding bosonic blocks in Jack polynomials, applying the superconformal Casimir operator to obtain linear constraints, and imposing the superconformal Ward identity—derived from the auxiliary R-symmetry variables—order by order in a radial expansion. The Ward identity is the mechanism that fixes the coefficients uniquely; the Casimir equation alone leaves the system underdetermined except for the D-type blocks.

What would settle it

Use the companion coefficient file for a long multiplet in a mixed correlator with external R-charges (1,2,2,3), expand the left-hand side of the Ward identity (3.21) to one radial order beyond the finite check performed in the paper, and verify that no Jack-polynomial coefficient remains; any nonzero remainder would mean the published coefficients are not the complete all-orders solution.

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Extended reading notes

Core claim

The central claim is that for SCFTs with SU(2) R-symmetry, the superconformal blocks of mixed half-BPS four-point functions are completely fixed by the superconformal Ward identity, as an expansion over bosonic conformal blocks with coefficients that are rational functions of the conformal data and of ε=(d−2)/2, independent of the spacetime dimension. Long multiplets and B- and D-type short multiplets contribute; A- and C-type multiplets are excluded. For D-type multiplets the paper gives closed coefficient formulas; for B-type and long multiplets the coefficients are tabulated and supplied in a companion file. Many coefficients are mapped into one another by the four accidental Z2 transformations (Δ,ℓ)→(−(ℓ+1),−(Δ+1)), Δ→−(Δ+D−4), ℓ→−(ℓ+(D−2)), and JR→−(JR+1), suggesting a hidden symmetry of the blocks.

Load-bearing premise

The listed coefficients are assumed to satisfy the Ward identity at every order, although only a finite-order check is shown; if a higher-order term violates the identity, the coefficient lists would be incomplete.

Editorial extensions

If this is right

  • The explicit blocks make mixed-correlator superconformal bootstrap calculations possible for external operators of arbitrary SU(2) R-charge, not just momentum maps or energy-momentum tensors.
  • Because the results are dimension-independent for 2<d≤6, the same blocks apply to 6D N=(1,0) SCFTs and their dimensional reductions, with only the parameter ε changing.
  • The selection rules are fixed: only long, B-, and D-type multiplets contribute, while A- and C-type multiplets are excluded from the block expansion of half-BPS four-point functions.
  • The coefficient relations under the four Z2 transformations imply a hidden symmetry of the superconformal Casimir that may admit a more compact closed form for the blocks.
  • The complete coefficient lists supply the input needed to write crossing equations for mixed half-BPS correlators, which is the natural next step for numerical bootstrap applications.

Reading between the lines

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

  • Beyond the paper: the same Ward-identity-plus-Casimir strategy should transfer to SCFTs with larger R-symmetry groups, where the Casimir system is again likely to be underdetermined and the Ward identity decisive.
  • Beyond the paper: the dimension-independent blocks could be evaluated at non-integer d, where no interacting SCFT exists but the bootstrap equations remain well defined, extending the reach of numerical searches.
  • Beyond the paper: a systematic search for a closed form invariant under the four Z2 transformations is a natural next step; if one exists, it would accelerate bootstrap codes and reveal the structure behind the long coefficient lists.
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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 derives superconformal blocks for four-point functions of four a priori distinct D-type (half-BPS) superconformal primaries in SCFTs with SU(2) R-symmetry, working in a dimension-independent way for 2 < d ≤ 6. The blocks are decomposed into bosonic conformal blocks times SU(2) R-symmetry harmonics, and the coefficients are fixed by combining the superconformal Casimir equation with the superconformal Ward identity. The authors solve the resulting linear constraints order by order using an expansion in Jack polynomials and radial coordinates, provide explicit coefficients for D-type, B-type, and long multiplets, show that A- and C-type multiplets do not contribute, and identify a web of linear transformations relating many of the coefficients. The main output is a set of coefficient lists, with an exhaustive list supplied in a Mathematica file attached to the arXiv submission.

Significance. If the claims are correct, the paper provides a substantial and useful generalization of earlier superconformal block computations: it goes beyond momentum-map or coincident-R-charge correlators to mixed correlators with arbitrary R-charges in theories with eight supercharges, uniformly for 3 ≤ d ≤ 6. The consistency checks against known results for D[1] and D[J] in lower dimensions are real supporting evidence, and the explicit identification of selection rules for A- and C-type multiplets is a useful byproduct. The paper also ships an exhaustive coefficient list in computer-readable form, which is valuable for bootstrap applications. The main weakness is that the all-orders completeness and uniqueness of the coefficient solution are asserted rather than fully demonstrated; this is a central claim, not just a presentation issue.

major comments (2)
  1. [Section 4, paragraph after Eq. (4.5)] The paper states: "If a solution is found to be valid up to some threshold, one can then easily check that it is satisfied to all orders by reinjecting it in the original equation and using the recursion relations (4.2) and (4.3)." However, the threshold is never specified, and the all-orders reinjection check is neither displayed in the text nor included in the Mathematica attachment, which contains the final coefficients rather than the verification. This matters because, as the paper itself notes in the B-type discussion and in Section 5, the type (II) Casimir equation is underdetermined for B-type and long multiplets, so uniqueness of the listed coefficients rests entirely on the Ward identity. The authors should supply either a closed induction argument using (4.2)-(4.3), or a verification script that checks the Ward identity and Casimir equations to arbitrarily high order, or at minimum state the finite threshold and exhibit the recursive step that proves propagation to all orders.
  2. [Section 4, linear system (4.5) and uniqueness claim] The abstract and Section 4 claim that the Casimir and Ward identities fix all coefficients uniquely, but the displayed procedure only solves a linear system order by order in the radial expansion. No rank analysis or triangularity argument is given to show that no new independent constraints appear at higher orders. In particular, for B-type and long multiplets the type (II) Casimir equation is underdetermined, so the uniqueness statement depends entirely on the Ward identity constraints at every order. The authors should either prove that the system is triangular in the order-by-order expansion or otherwise demonstrate that the solution space has dimension one at each order; otherwise the claim of uniqueness is stronger than what is shown.
minor comments (4)
  1. [Footnote 2, page 3] "We excluded≤2 as in that case some of the generators may decouple" appears to be missing the spacetime dimension variable; it should read "excluded d ≤ 2".
  2. [Section 2.2, Eq. (2.22)] The text says the SU(2)_R harmonics a priori depend on J1+J2, but Eq. (2.22) as written depends on J12, J34, and J. This is presumably because the a1 = J1+J2 normalization has already been used; please make this explicit so the reader does not misread Eq. (2.22) as the most general expression.
  3. [Section 4, coefficient tables] The printed coefficients in Appendix D contain both ε and ℓ in close proximity, and the Mathematica file is described only briefly. A short note explaining the notation in the file, or a table matching the file's variable names to the paper's, would greatly improve usability.
  4. [Throughout] There are occasional stylistic slips such as "in section (4)" instead of "Section 4" and "the holomorphic/anti-holomorphic variables" being used inconsistently. These do not affect the physics but should be cleaned up in a revision.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the superconformal blocks are fixed by independent Ward-identity and Casimir constraints, with only a non-load-bearing self-reference to a future work.

full rationale

The derivation is self-contained. The block coefficients f^J are defined by the OPE decomposition (2.14)-(2.15), and are then fixed by two independent sets of constraints: the superconformal Casimir equation (3.17) and the superconformal Ward identity (3.21). Neither constraint is constructed from the coefficients being sought; the Ward identity follows from the pole structure of superconformal transformations in superspace (3.18)-(3.19), and the Casimir equation follows from the superconformal quadratic Casimir acting on the four-point function. Solving the resulting linear system (4.5) with the primary coefficient normalized to one determines the remaining coefficients as ratios; no parameter is fitted to the output, and the known-limit reductions to earlier results for momentum-map and four-dimensional blocks are independent checks. The paper explicitly states that the type (II) Casimir equation alone is 'no longer strong enough to fix all of the coefficients' for B-type and long multiplets, and that the Ward identity supplies the missing uniqueness, which is a genuine additional input rather than a repackaging. The only self-reference, [68], is an unpublished follow-up announced in the conclusions and plays no role in the derivation. The main flagged limitation is the all-orders completeness assertion in Section 4: 'If a solution is found to be valid up to some threshold, one can then easily check that it is satisfied to all orders by reinjecting it in the original equation and using the recursion relations (4.2) and (4.3).' The threshold and the reinjection check are not shown, so the exhaustive coefficient list is verified only up to an unspecified truncation. That is a completeness gap, not a circularity, because it concerns the proof of exhaustiveness rather than the logical dependence of the result on its own inputs.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central derivation introduces no fitted parameters: all coefficients are rational functions of the external SU(2) charges, the primary data (Δ,ℓ,J_R), and ε=(d-2)/2, with no constants matched to the final answer. The inputs are the superconformal multiplet classification of [19,20], the standard Ward identity of [32,33], and properties of Jack polynomials; these are external prerequisites, not assumptions whose conclusion is the result. The only ad hoc assumption is the assertion that finite-order solutions verified via recursion extend to all orders.

assumptions (5)
  • domain assumption The superconformal multiplet classification of [19,20] (A, B, C, D, L types) with shortening conditions (1.1) is correct and complete for SCFTs with SU(2) R-symmetry and eight supercharges in 2<d≤6.
    Used throughout Section 3 to enumerate the possible states, including table 1, and to select which multiplets can appear in the OPE.
  • domain assumption The four-point function of D-type primaries can be expanded as a finite sum over bosonic conformal blocks corresponding to states in the exchanged multiplet with R-charge transfers JR-2..JR+2 and dimension shifts up to Δ+4 (equation 2.15).
    Central ansatz (2.15) and (2.24) relies on representation theory of the superconformal algebra, cited to [19,20].
  • domain assumption The superconformal Ward identity (3.21), in the frame of [32,33], imposes all constraints from supersymmetry on the four-point function; its solution determines the block completely.
    Used in Sections 3.2 and 4 to fix coefficients; for non-coincident external charges the identity is extended to the J12,J34-dependent case, but its completeness is assumed.
  • ad hoc to paper The solution of the linearised Ward-identity constraints up to a finite order in the radial expansion extends to all orders via the recursion relations (4.2)-(4.3).
    The paper asserts this in Section 4 but does not show the verification; this is the weakest assumption in the derivation.
  • standard math The Jack polynomial and hypergeometric identities used to evaluate the differential operators (equations (4.4), (C.13)-(C.17)) are correct.
    Standard properties of Jack polynomials; cited to [32] and collected in appendix C.

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Cite this review

Pith. "Pith review of Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry." pith.science (2026). https://pith.science/paper/UTIYFL6E

@misc{pith2026190802768,
  author       = {Pith},
  title        = {Pith review of: Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UTIYFL6E}},
  note         = {Machine review of arXiv:1908.02768}
}
abstract

For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks uniquely in a dimension-independent way. In addition we find that many of the resulting coefficients are related through a web of linear transformations of the conformal data.

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Works this paper leans on

68 extracted references · 18 canonical work pages

  1. [1]

    Luscher, Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions , Commun

    M. Luscher, Operator product expansions on the vacuum in conformal quantum field theory in two spacetime dimensions , Commun. Math. Phys. 50 (1976) 23

    work page 1976

  2. [2]

    Mack, Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory , Commun

    G. Mack, Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory , Commun. Math. Phys. 53 (1977) 155

    work page 1977

  3. [3]

    F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B599 (2001) 459 [ hep-th/0011040]

    arXiv 2001

  4. [4]

    F. A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B678 (2004) 491 [ hep-th/0309180]

    arXiv 2004

  5. [5]

    Rattazzi, V

    R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 12 (2008) 031 [ 0807.0004]

    arXiv 2008

  6. [6]

    Rychkov, EPFL Lectures on Conformal Field Theory in ≥ 3 Dimensions, Briefs in Physics

    S. Rychkov, EPFL Lectures on Conformal Field Theory in ≥ 3 Dimensions, Briefs in Physics. Springer, 2016, 10.1007/978-3-319-43626-5, [ 1601.05000]

    arXiv 2016

  7. [7]

    D. Simmons-Duffin, The Conformal Bootstrap, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015): Boulder, CO, USA, June 1-26, 2015 , pp. 1–74, 2017, 1602.07982, DOI. 37

    arXiv 2015

  8. [8]

    Poland, S

    D. Poland, S. Rychkov and A. Vichi, The Conformal Bootstrap: Theory, Numerical Techniques, and Applications, 1805.04405

    arXiv

Show all 68 references
  1. [9]

    S. M. Chester, Weizmann Lectures on the Numerical Conformal Bootstrap , 1907.05147

    1907 arXiv

  2. [10]

    Ferrara, A

    S. Ferrara, A. F. Grillo and R. Gatto, Manifestly conformal covariant operator-product expansion, Lett. Nuovo Cim. 2S2 (1971) 1363

    1971

  3. [11]

    A. A. Migdal, Conformal invariance and bootstrap, Phys. Lett. 37B (1971) 386

    1971

  4. [12]

    Ferrara, A

    S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, Covariant expansion of the conformal four-point function, Nucl. Phys. B49 (1972) 77

    1972

  5. [13]

    Ferrara, A

    S. Ferrara, A. F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion, Annals Phys. 76 (1973) 161

    1973

  6. [14]

    A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory , Zh. Eksp. Teor. Fiz. 66 (1974) 23

    1974

  7. [15]

    Ferrara, R

    S. Ferrara, R. Gatto and A. F. Grillo, Properties of Partial Wave Amplitudes in Conformal Invariant Field Theories , Nuovo Cim. A26 (1975) 226

    1975

  8. [16]

    Ferrara, R

    S. Ferrara, R. Gatto and A. F. Grillo, Positivity Restrictions on Anomalous Dimensions, Phys. Rev. D9 (1974) 3564

    1974

  9. [17]

    Ferrara, A

    S. Ferrara, A. F. Grillo, R. Gatto and G. Parisi, Analyticity properties and asymptotic expansions of conformal covariant green’s functions , Nuovo Cim. A19 (1974) 667

    1974

  10. [18]

    V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova and I. T. Todorov, Harmonic Analysis on the n-Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory , Lect. Notes Phys. 63 (1977) 1

    1977

  11. [19]

    Buican, J

    M. Buican, J. Hayling and C. Papageorgakis, Aspects of Superconformal Multiplets in D >4, JHEP 11 (2016) 091 [ 1606.00810]

    2016 arXiv

  12. [20]

    Cordova, T

    C. Cordova, T. T. Dumitrescu and K. Intriligator, Multiplets of Superconformal Symmetry in Diverse Dimensions , 1612.00809

    arXiv

  13. [21]

    S. M. Chester, J. Lee, S. S. Pufu and R. Yacoby, Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap, JHEP 03 (2015) 130 [ 1412.0334]. 38

    2015 arXiv

  14. [22]

    Liendo and C

    P. Liendo and C. Meneghelli, Bootstrap equations forN = 4 SYM with defects , JHEP 01 (2017) 122 [ 1608.05126]

    2017 arXiv

  15. [23]

    C. Beem, M. Lemos, P. Liendo, L. Rastelli and B. C. van Rees, TheN = 2 superconformal bootstrap, JHEP 03 (2016) 183 [ 1412.7541]

    2016 arXiv

  16. [24]

    Lemos and P

    M. Lemos and P. Liendo, BootstrappingN = 2 chiral correlators, JHEP 01 (2016) 025 [1510.03866]

    2016 arXiv

  17. [25]

    Chang, M

    C.-M. Chang, M. Fluder, Y.-H. Lin and Y. Wang, Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey , JHEP 03 (2018) 123 [ 1710.08418]

    2018 arXiv

  18. [26]

    Chang and Y.-H

    C.-M. Chang and Y.-H. Lin, Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions) , JHEP 08 (2017) 128 [ 1705.05392]

    2017 arXiv

  19. [27]

    Bobev, E

    N. Bobev, E. Lauria and D. Mazac, Superconformal Blocks for SCFTs with Eight Supercharges, JHEP 07 (2017) 061 [ 1705.08594]

    2017 arXiv

  20. [28]

    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 [1312.5344]

    2015 arXiv

  21. [29]

    N. B. Agmon, S. M. Chester and S. S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 [ 1711.07343]

    2018 arXiv

  22. [30]

    N. B. Agmon, S. M. Chester and S. S. Pufu, The M-theory Archipelago, 1907.13222

    1907 arXiv

  23. [31]

    F. A. Dolan and H. Osborn, Superconformal symmetry, correlation functions and the operator product expansion, Nucl. Phys. B629 (2002) 3 [ hep-th/0112251]

    2002 arXiv

  24. [32]

    F. A. Dolan, L. Gallot and E. Sokatchev, On four-point functions of 1/2-BPS operators in general dimensions , JHEP 09 (2004) 056 [ hep-th/0405180]

    2004 arXiv

  25. [33]

    Nirschl and H

    M. Nirschl and H. Osborn, Superconformal Ward identities and their solution , Nucl. Phys. B711 (2005) 409 [ hep-th/0407060]

    2005 arXiv

  26. [34]

    Bobev, S

    N. Bobev, S. El-Showk, D. Mazac and M. F. Paulos, Bootstrapping SCFTs with Four Supercharges, JHEP 08 (2015) 142 [ 1503.02081]

    2015 arXiv

  27. [35]

    Seiberg and E

    N. Seiberg and E. Witten, Comments on string dynamics in six-dimensions , Nucl. Phys. B471 (1996) 121 [ hep-th/9603003]. 39

    1996 arXiv

  28. [36]

    O. J. Ganor and A. Hanany, Small E(8) instantons and tensionless noncritical strings , Nucl. Phys. B474 (1996) 122 [ hep-th/9602120]

    1996 arXiv

  29. [37]

    Gaiotto, N=2 dualities, JHEP 08 (2012) 034 [ 0904.2715]

    D. Gaiotto, N=2 dualities, JHEP 08 (2012) 034 [ 0904.2715]

    2012 arXiv

  30. [38]

    J. J. Heckman and C. Vafa, Fine Tuning, Sequestering, and the Swampland , 1905.06342

    1905 arXiv

  31. [39]

    Nahm, Supersymmetries and their Representations , Nucl

    W. Nahm, Supersymmetries and their Representations , Nucl. Phys. B135 (1978) 149

    1978

  32. [40]

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

    2003 arXiv

  33. [41]

    F. A. Dolan and H. Osborn, Conformal Partial Waves: Further Mathematical Results , 1108.6194

    arXiv

  34. [42]

    Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv

    S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 783 [ hep-th/9712074]

    1998 arXiv

  35. [43]

    Ferrara and E

    S. Ferrara and E. Sokatchev, Universal properties of superconformal OPEs for 1/2 BPS operators in 3≤D≤ 6, New J. Phys. 4 (2002) 2 [ hep-th/0110174]

    2002 arXiv

  36. [44]

    V. K. Dobrev and V. B. Petkova, All Positive Energy Unitary Irreducible Representations of Extended Conformal Supersymmetry , Phys. Lett. 162B (1985) 127

    1985

  37. [45]

    V. K. Dobrev and V. B. Petkova, On The Group Theoretical Approach To Extended Conformal Supersymmetry: Classification Of Multiplets , Lett. Math. Phys. 9 (1985) 287

    1985

  38. [46]

    V. K. Dobrev and V. B. Petkova, Group Theoretical Approach to Extended Conformal Supersymmetry: Function Space Realizations and Invariant Differential Operators , Fortsch. Phys. 35 (1987) 537

    1987

  39. [47]

    Bhattacharya, S

    J. Bhattacharya, S. Bhattacharyya, S. Minwalla and S. Raju, Indices for Superconformal Field Theories in 3,5 and 6 Dimensions , JHEP 02 (2008) 064 [0801.1435]

    2008 arXiv

  40. [48]

    Cordova, T

    C. Cordova, T. T. Dumitrescu and K. Intriligator, Deformations of Superconformal Theories, JHEP 11 (2016) 135 [ 1602.01217]

    2016 arXiv

  41. [49]

    Hogervorst and S

    M. Hogervorst and S. Rychkov, Radial Coordinates for Conformal Blocks , Phys. Rev. D87 (2013) 106004 [ 1303.1111]. 40

    2013 arXiv

  42. [50]

    M. S. Costa, T. Hansen, J. Penedones and E. Trevisani, Radial expansion for spinning conformal blocks, JHEP 07 (2016) 057 [ 1603.05552]

    2016 arXiv

  43. [51]

    F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N) vector models, JHEP 06 (2014) 091 [ 1307.6856]

    2014 arXiv

  44. [52]

    F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping Mixed Correlators in the 3D Ising Model, JHEP 11 (2014) 109 [ 1406.4858]

    2014 arXiv

  45. [53]

    Penedones, E

    J. Penedones, E. Trevisani and M. Yamazaki, Recursion Relations for Conformal Blocks, JHEP 09 (2016) 070 [ 1509.00428]

    2016 arXiv

  46. [54]

    Rattazzi, S

    R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4D Conformal Field Theories with Global Symmetry, J. Phys. A44 (2011) 035402 [ 1009.5985]

    2011 arXiv

  47. [55]

    S. M. Chester, J. Lee, S. S. Pufu and R. Yacoby, TheN = 8 superconformal bootstrap in three dimensions, JHEP 09 (2014) 143 [ 1406.4814]

    2014 arXiv

  48. [56]

    A. L. Fitzpatrick, J. Kaplan, Z. U. Khandker, D. Li, D. Poland and D. Simmons-Duffin, Covariant Approaches to Superconformal Blocks, JHEP 08 (2014) 129 [ 1402.1167]

    2014 arXiv

  49. [57]

    F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Bootstrapping the O(N) Archipelago, JHEP 11 (2015) 106 [ 1504.07997]

    2015 arXiv

  50. [58]

    F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Precision Islands in the Ising and O(N) Models, JHEP 08 (2016) 036 [ 1603.04436]

    2016 arXiv

  51. [59]

    Li and N

    Z. Li and N. Su, Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models, JHEP 04 (2017) 098 [ 1607.07077]

    2017 arXiv

  52. [60]

    D. Li, D. Meltzer and A. Stergiou, Bootstrapping mixed correlators in 4D N = 1 SCFTs, JHEP 07 (2017) 029 [ 1702.00404]

    2017 arXiv

  53. [61]

    Rong and N

    J. Rong and N. Su, Bootstrapping minimalN = 1 superconformal field theory in three dimensions, 1807.04434

    arXiv

  54. [62]

    S. R. Kousvos and A. Stergiou, Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories, SciPost Phys. 6 (2019) 035 [ 1810.10015]

    2019 arXiv

  55. [63]

    C. Beem, M. Lemos, L. Rastelli and B. C. van Rees, The (2, 0) superconformal bootstrap, Phys. Rev. D93 (2016) 025016 [ 1507.05637]. 41

    2016 arXiv

  56. [64]

    J. J. Heckman, D. R. Morrison and C. Vafa, On the Classification of 6D SCFTs and Generalized ADE Orbifolds, JHEP 05 (2014) 028 [ 1312.5746]

    2014 arXiv

  57. [65]

    J. J. Heckman, D. R. Morrison, T. Rudelius and C. Vafa, Atomic Classification of 6D SCFTs, Fortsch. Phys. 63 (2015) 468 [ 1502.05405]

    2015 arXiv

  58. [66]

    Bhardwaj, D

    L. Bhardwaj, D. R. Morrison, Y. Tachikawa and A. Tomasiello, The frozen phase of F-theory, JHEP 08 (2018) 138 [ 1805.09070]

    2018 arXiv

  59. [67]

    J. J. Heckman and T. Rudelius, Top Down Approach to 6D SCFTs , J. Phys. A52 (2019) 093001 [ 1805.06467]

    2019 arXiv

  60. [68]

    Baume, M

    F. Baume, M. Fuchs and C. Lawrie, To Appear, . 42

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.