pith. sign in

arxiv: 2605.16497 · v1 · pith:LX7C35DPnew · submitted 2026-05-15 · ✦ hep-th

5d Trinions and Tetraons

Mario De Marco , Michele Del Zotto , Michele Graffeo , Andrea Sangiovanni This is my paper

Pith reviewed 2026-05-20 16:23 UTC · model grok-4.3

classification ✦ hep-th
keywords 5d SCFTsM-theory geometric engineeringgeneralized quiverstrinionstetraonsflavor symmetryinstantonic symmetry enhancementsingular geometries
0
0 comments X

The pith

M-theory geometric engineering constructs trinions and tetraons as non-linear 5d SCFTs with type D flavor symmetry.

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

The paper extends an atomic classification of 5d superconformal field theories beyond linear bifundamental conformal matter. It uses M-theory geometric engineering to build trinions and tetraons that carry type D flavor symmetries and appear as non-linear generalized quivers. These objects exhibit new patterns of instantonic symmetry enhancement, and their fusions generate singular geometries that are frequently non-toric and non-complete intersections. The same construction rules out analogous trinions and tetraons with type E flavor symmetry. A reader would care because the result enlarges the set of known building blocks and fusion rules for 5d SCFTs.

Core claim

We generalize such picture employing M-theory geometric engineering to construct trinions and tetraon 5d SCFTs with flavor symmetry of type D. They correspond to non-linear generalized quivers displaying novel patterns of instantonic symmetry enhancement, and their fusion produces singular geometries that often are non-toric non-complete intersections. Finally, within our setup, we rule out trinions and tetraons of type E.

What carries the argument

Non-linear generalized quivers obtained via M-theory geometric engineering, which realize instantonic symmetry enhancement for D-type flavor symmetries and fuse into non-toric singular geometries.

If this is right

  • Trinions and tetraons with type D flavor symmetry exist as 5d SCFTs.
  • These non-linear quivers display novel patterns of instantonic symmetry enhancement.
  • Fusions of trinions and tetraons produce singular geometries that are often non-toric and non-complete intersections.
  • Trinions and tetraons of type E are ruled out within the M-theory geometric engineering setup.

Where Pith is reading between the lines

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

  • The non-linear building blocks may allow a fuller atomic classification that includes branched quiver structures beyond linear ones.
  • The appearance of non-toric geometries hints at new families of Calabi-Yau singularities usable for engineering 5d SCFTs.
  • The exclusion of E-type structures suggests that only certain Dynkin types permit such non-linear fusions in five dimensions.

Load-bearing premise

The atomic classification scheme that identifies indecomposable building blocks and fuses them into 5d SCFTs extends without obstruction to non-linear trinion and tetraon configurations.

What would settle it

An explicit M-theory geometry realizing a consistent trinion or tetraon with E-type flavor symmetry would falsify the exclusion of type E structures.

Figures

Figures reproduced from arXiv: 2605.16497 by Andrea Sangiovanni, Mario De Marco, Michele Del Zotto, Michele Graffeo.

Figure 1
Figure 1. Figure 1: Gauge theory phase for a trinion (resp. tetraon) theory with flavor symmetry [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Toric diagram for the Tn theories. The corresponding 5d SCFTs have tri-valent A ⊕3 n−1 UV flavor symmetry (with possible non-abelian enhancement) and non-trivial gauge content. This is a clear consequence of the pattern of non-compact singular lines in the CY3. An additional non-toric family (with one toric family member) of singularities that engineers 5d CM theories with n flavor factors of type A is giv… view at source ↗
Figure 3
Figure 3. Figure 3: Toric diagram for the SP P theory. Nonetheless, it is straightforward to observe that non-trivial interacting n-valent 5d SCFTs with ⊕i=1,...,nAri−1 flavor symmetry (and arbitrary positive n) can be constructed, 6For the definition of canonical singularities, we refer to [93]. 10 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Gluing procedures to obtain 4-valent (top) and 5-valent (bottom) 5d toric [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The resolution of the singular 5d CM threefolds either gives rise to a special [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Pictorial representation of Xe. The compact curves are arranged like a Dk Dynkin diagram. node of [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The novel bifundamental, trinion and tetraon theories are not irreducible: [PITH_FULL_IMAGE:figures/full_fig_p025_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Fusion of 5d SCFTs, from the CY3 perspective. [PITH_FULL_IMAGE:figures/full_fig_p028_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Linear gluings of 5d bifundamental CM produce generalized bifundamental 5d [PITH_FULL_IMAGE:figures/full_fig_p029_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Linear gluings of 5d non-toric trinion CM do not admit a generalized quiver [PITH_FULL_IMAGE:figures/full_fig_p030_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: for the gluing of a trinion. We will return on the matter of whether these generalized quiver phases admit a 5d SCFT limit in Section 4.2.2. The remaining part of this Section is devoted to providing explicit examples of the above-mentioned gaugings, namely to identifying the allowed dashed flavor nodes in [PITH_FULL_IMAGE:figures/full_fig_p037_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Pictorial representation of the partial resolution of [PITH_FULL_IMAGE:figures/full_fig_p046_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Balanced quiver of type D, labelled by the weight in (A.3). Notice that the quiver can be labelled by the following weight of the Lie algebra of type D:   0 0 . . . 0 2 0   (A.3) For a generic algebra of type D, this is the only weight that corresponds to a balanced quiver with gauge multiplicities 1 or 224. Any other weight produces at least one gauge node with multiplicity 3. This would result in a … view at source ↗
Figure 14
Figure 14. Figure 14: Pictorial representation of the partially resolved and singular phase of the [PITH_FULL_IMAGE:figures/full_fig_p053_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Pictorial representation of the crepant blow-up of [PITH_FULL_IMAGE:figures/full_fig_p062_15.png] view at source ↗
read the original abstract

Recently, an atomic classification scheme of 5d SCFTs has been proposed, relying on the identification of indecomposable building blocks that can be fused together to produce large classes of 5d SCFTs. These novel SCFTs are known as bifundamental 5d conformal matter theories, and their fusion produces linear generalized quivers. We generalize such picture employing M-theory geometric engineering to construct trinions and tetraon 5d SCFTs with flavor symmetry of type D. They correspond to non-linear generalized quivers displaying novel patterns of instantonic symmetry enhancement, and their fusion produces singular geometries that often are non-toric non-complete intersections. Finally, within our setup, we rule out trinions and tetraons of type E.

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

0 major / 2 minor

Summary. The manuscript extends the atomic classification of 5d SCFTs by using M-theory geometric engineering to construct trinions and tetraons with D-type flavor symmetry. These are realized as non-linear generalized quivers exhibiting novel instantonic symmetry enhancements; their fusions yield singular geometries that are typically non-toric and non-complete intersections. The same framework is used to rule out trinions and tetraons of type E.

Significance. If the constructions are valid, the work meaningfully enlarges the set of known 5d SCFTs by moving beyond linear quivers to non-linear configurations. The explicit exclusion of E-type cases provides a useful internal consistency test, and the appearance of non-toric geometries from fusion illustrates new features accessible via geometric engineering. Credit is due for grounding the results in established M-theory techniques rather than parameter fitting.

minor comments (2)
  1. The abstract would be clearer if it briefly indicated the specific M-theory brane configurations or Calabi-Yau singularities employed for the D-type constructions.
  2. Notation for the instantonic symmetry enhancements could be introduced once in the main text and then used consistently to avoid minor ambiguity when comparing trinion and tetraon cases.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, accurate summary of the results on 5d trinions and tetraons with D-type flavor symmetry, and recommendation to accept. We are pleased that the significance of extending beyond linear quivers and the consistency check from excluding E-type cases was recognized.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper generalizes an existing atomic classification of 5d SCFTs via M-theory geometric engineering to construct trinions and tetraons with D-type flavor symmetry, deriving novel instantonic enhancements and non-toric geometries directly from the geometric setup. The central claims rest on explicit constructions and an explicit ruling-out of E-type cases within the same framework rather than on parameter fits, self-definitions, or load-bearing self-citations that reduce to unverified inputs. The starting assumption of extending the classification is stated as such and does not force the reported results by construction. The derivation remains self-contained against external geometric benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on the standard assumptions of M-theory geometric engineering for 5d SCFTs, including the existence of suitable Calabi-Yau threefolds and the correspondence between geometric singularities and field theory data. No new free parameters or invented entities are introduced beyond those in the referenced atomic classification scheme.

axioms (2)
  • domain assumption M-theory geometric engineering correctly captures the spectrum and symmetries of 5d SCFTs via Calabi-Yau compactifications.
    Invoked throughout the construction of trinions and tetraons.
  • domain assumption The atomic classification scheme of indecomposable building blocks extends to non-linear fusions without additional obstructions.
    Basis for generalizing from linear quivers to trinions and tetraons.

pith-pipeline@v0.9.0 · 5656 in / 1430 out tokens · 53357 ms · 2026-05-20T16:23:34.038567+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

101 extracted references · 101 canonical work pages · 48 internal anchors

  1. [1]

    String Theory Dynamics In Various Dimensions

    E. Witten, “String theory dynamics in various dimensions,”Nucl. Phys. B443 (1995) 85–126,hep-th/9503124

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  2. [2]

    Open P-Branes

    A. Strominger, “Open p-branes,”Phys. Lett. B383(1996) 44–47,hep-th/9512059

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  3. [3]

    Five-branes And $M$-Theory On An Orbifold

    E. Witten, “Five-branes and M theory on an orbifold,”Nucl. Phys. B463(1996) 383–397,hep-th/9512219

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  4. [4]

    Small $E_8$ Instantons and Tensionless Non-critical Strings

    O. J. Ganor and A. Hanany, “Small E(8) instantons and tensionless noncritical strings,”Nucl. Phys. B474(1996) 122–140,hep-th/9602120

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  5. [5]

    Non-trivial Fixed Points of The Renormalization Group in Six Dimensions

    N. Seiberg, “Nontrivial fixed points of the renormalization group in six-dimensions,” Phys. Lett. B390(1997) 169–171,hep-th/9609161

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  6. [6]

    Five dimensional susy field theories, non-trivial fixed points and string dynamics,

    N. Seiberg, “Five dimensional susy field theories, non-trivial fixed points and string dynamics,”Physics Letters B388(Nov, 1996) 753–760

    work page 1996

  7. [7]

    Extremal transitions and five-dimensional super- symmetric field theories,

    D. R. Morrison and N. Seiberg, “Extremal transitions and five-dimensional super- symmetric field theories,”Nuclear Physics B483(Jan, 1997) 229–247

    work page 1997

  8. [8]

    Small Instantons, del Pezzo Surfaces and Type I' theory

    M. R. Douglas, S. H. Katz, and C. Vafa, “Small instantons, Del Pezzo surfaces and type I-prime theory,”Nucl. Phys. B497(1997) 155–172,hep-th/9609071

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  9. [9]

    Supersymmetries and their Representations,

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

    work page 1978

  10. [10]

    Atomic Classification of 6D SCFTs

    J. J. Heckman, D. R. Morrison, T. Rudelius, and C. Vafa, “Atomic Classification of 6D SCFTs,”Fortsch. Phys.63(2015) 468–530,1502.05405

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  11. [11]

    5d Conformal matter,

    M. De Marco, M. Del Zotto, M. Graffeo, and A. Sangiovanni, “5d Conformal matter,”JHEP05(2024) 306,2311.04984

    work page arXiv 2024

  12. [12]

    Branes, Calabi-Yau Spaces, and Toroidal Compactification of the N=1 Six-Dimensional E_8 Theory

    O. J. Ganor, D. R. Morrison, and N. Seiberg, “Branes, Calabi-Yau spaces, and toroidal compactification of the N=1 six-dimensional E(8) theory,”Nucl. Phys. B 487(1997) 93–127,hep-th/9610251

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  13. [13]

    Branes, Superpotentials and Superconformal Fixed Points

    O. Aharony and A. Hanany, “Branes, superpotentials and superconformal fixed points,”Nucl. Phys. B504(1997) 239–271,hep-th/9704170

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  14. [14]

    Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams

    O. Aharony, A. Hanany, and B. Kol, “Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams,”JHEP01(1998) 002,hep-th/9710116. 64

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  15. [15]

    Five-branes, Seven-branes and Five-dimensional E_n field theories

    O. DeWolfe, A. Hanany, A. Iqbal, and E. Katz, “Five-branes, seven-branes and five-dimensional E(n) field theories,”JHEP03(1999) 006,hep-th/9902179

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  16. [16]

    Five-dimensional supersymmetric gauge theories and degenerations of calabi-yau spaces,

    K. Intriligator, D. R. Morrison, and N. Seiberg, “Five-dimensional supersymmetric gauge theories and degenerations of calabi-yau spaces,”Nuclear Physics B497 (Jul, 1997) 56–100

    work page 1997

  17. [17]

    Branes and toric geometry,

    N. C. Leung and C. Vafa, “Branes and toric geometry,” 1997

    work page 1997

  18. [18]

    Towards Classification of 5d SCFTs: Single Gauge Node,

    P. Jefferson, H.-C. Kim, C. Vafa, and G. Zafrir, “Towards Classification of 5d SCFTs: Single Gauge Node,”SciPost Phys.14(2023) 122,1705.05836

    work page arXiv 2023

  19. [19]

    On Geometric Classification of 5d SCFTs

    P. Jefferson, S. Katz, H.-C. Kim, and C. Vafa, “On Geometric Classification of 5d SCFTs,”JHEP04(2018) 103,1801.04036

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  20. [20]

    6D SCFTs and Phases of 5D Theories

    M. Del Zotto, J. J. Heckman, and D. R. Morrison, “6D SCFTs and Phases of 5D Theories,”JHEP09(2017) 147,1703.02981

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  21. [21]

    Classifying5d SCFTs via6d SCFTs: Rank one,

    L. Bhardwaj and P. Jefferson, “Classifying5d SCFTs via6d SCFTs: Rank one,” JHEP07(2019) 178,1809.01650. [Addendum: JHEP 01, 153 (2020)]

    work page arXiv 2019

  22. [22]

    Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank,

    L. Bhardwaj and P. Jefferson, “Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank,”JHEP10(2019) 282,1811.10616

    work page arXiv 2019

  23. [23]

    Do all 5d SCFTs descend from 6d SCFTs?,

    L. Bhardwaj, “Do all 5d SCFTs descend from 6d SCFTs?,”JHEP04(2021) 085, 1912.00025

    work page arXiv 2021

  24. [24]

    Classification of 5dN = 1 gauge theories,

    L. Bhardwaj and G. Zafrir, “Classification of 5dN = 1 gauge theories,”JHEP12 (2020) 099,2003.04333

    work page arXiv 2020

  25. [25]

    Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States,

    F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki, and Y.-N. Wang, “Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States,” JHEP11(2019) 068,1907.05404

    work page arXiv 2019

  26. [26]

    Fibers add flavor. part II. 5d SCFTs, gauge theories, and dualities,

    F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki, and Y.-N. Wang, “Fibers add flavor. part II. 5d SCFTs, gauge theories, and dualities,”Journal of High Energy Physics2020(mar, 2020)

    work page 2020

  27. [27]

    Webs of five-branes and N=2 superconformal field theories

    F. Benini, S. Benvenuti, and Y. Tachikawa, “Webs of five-branes and N=2 super- conformal field theories,”JHEP09(2009) 052,0906.0359. 65

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  28. [28]

    5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory

    O. Bergman, D. Rodríguez-Gómez, and G. Zafrir, “5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory,”JHEP03(2014) 112,1311.4199

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  29. [29]

    Duality and enhancement of symmetry in 5d gauge theories

    G. Zafrir, “Duality and enhancement of symmetry in 5d gauge theories,”JHEP12 (2014) 116,1408.4040

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  30. [30]

    6d SCFTs, 5d Dualities and Tao Web Diagrams

    H. Hayashi, S.-S. Kim, K. Lee, and F. Yagi, “6d SCFTs, 5d Dualities and Tao Web Diagrams,”JHEP05(2019) 203,1509.03300

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  31. [31]

    A new 5d description of 6d D-type minimal conformal matter

    H. Hayashi, S.-S. Kim, K. Lee, M. Taki, and F. Yagi, “A new 5d description of 6d D-type minimal conformal matter,”JHEP08(2015) 097,1505.04439

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  32. [32]

    5d fixed points from brane webs and O7-planes

    O. Bergman and G. Zafrir, “5d fixed points from brane webs and O7-planes,” JHEP12(2015) 163,1507.03860

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  33. [33]

    Dualities and 5-brane webs for 5d rank 2 SCFTs

    H. Hayashi, S.-S. Kim, K. Lee, and F. Yagi, “Dualities and 5-brane webs for 5d rank 2 SCFTs,”JHEP12(2018) 016,1806.10569

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  34. [34]

    5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories

    H. Hayashi, S.-S. Kim, K. Lee, and F. Yagi, “5-brane webs for 5dN = 1 G2 gauge theories,”JHEP03(2018) 125,1801.03916

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  35. [35]

    Rank-3 antisymmetric matter on 5-brane webs

    H. Hayashi, S.-S. Kim, K. Lee, and F. Yagi, “Rank-3 antisymmetric matter on 5-brane webs,”JHEP05(2019) 133,1902.04754

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  36. [36]

    Complete prepotential for 5dN = 1 superconformal field theories,

    H. Hayashi, S.-S. Kim, K. Lee, and F. Yagi, “Complete prepotential for 5dN = 1 superconformal field theories,”Journal of High Energy Physics2020(Feb, 2020)

    work page 2020

  37. [37]

    The Cat’s Cradle: deforming the higher rank E1 and ˜E1 theories,

    O. Bergman and D. Rodríguez-Gómez, “The Cat’s Cradle: deforming the higher rank E1 and ˜E1 theories,”JHEP02(2021) 122,2011.05125

    work page arXiv 2021

  38. [38]

    Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs,

    V. Alexeev, H. Argüz, and P. Bousseau, “Non-toric brane webs, Calabi-Yau 3-folds, and 5d SCFTs,”2410.04714

    work page arXiv

  39. [39]

    Twin theories, polytope mutations and quivers for GTPs,

    S. Franco and R.-K. Seong, “Twin theories, polytope mutations and quivers for GTPs,”JHEP07(2023) 034,2302.10951

    work page arXiv 2023

  40. [40]

    The geometry of GTPs and 5d SCFTs,

    G. Arias-Tamargo, S. Franco, and D. Rodríguez-Gómez, “The geometry of GTPs and 5d SCFTs,”JHEP07(2024) 159,2403.09776

    work page arXiv 2024

  41. [41]

    The 5d tangram: brane webs, 7-branes and primitive T-cones,

    I. Carreño Bolla, S. Franco, and D. Rodríguez-Gómez, “The 5d tangram: brane webs, 7-branes and primitive T-cones,”JHEP05(2025) 175,2411.01510. 66

    work page arXiv 2025

  42. [42]

    Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations,

    H.-C. Kim, M. Kim, S.-S. Kim, K. Lee, and X. Wang, “Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations,”2503.15591

    work page arXiv

  43. [43]

    Three dimensional canonical singularity and five dimensional N=1 SCFT

    D.XieandS.-T.Yau, “Threedimensionalcanonicalsingularityandfivedimensional N= 1 SCFT,”JHEP06(2017) 134,1704.00799

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  44. [44]

    Coulomb and Higgs Branches from Canonical Singularities: Part 0,

    C. Closset, S. Schafer-Nameki, and Y.-N. Wang, “Coulomb and Higgs Branches from Canonical Singularities: Part 0,”JHEP02(2021) 003,2007.15600

    work page arXiv 2021

  45. [45]

    5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities,

    C. Closset, S. Giacomelli, S. Schafer-Nameki, and Y.-N. Wang, “5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities,”JHEP05(2021) 274, 2012.12827

    work page arXiv 2021

  46. [46]

    CoulombandHiggsbranchesfrom canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions,

    C.Closset, S.Schäfer-Nameki, andY.-N.Wang, “CoulombandHiggsbranchesfrom canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions,” JHEP04(2022) 061,2111.13564

    work page arXiv 2022

  47. [47]

    Higgs branches of 5d rank-zero theories from geometry,

    A. Collinucci, M. De Marco, A. Sangiovanni, and R. Valandro, “Higgs branches of 5d rank-zero theories from geometry,”JHEP10(2021), no. 18, 018,2105.12177

    work page arXiv 2021

  48. [48]

    Genus zero Gopakumar-Vafa invariants from open strings,

    A. Collinucci, A. Sangiovanni, and R. Valandro, “Genus zero Gopakumar-Vafa invariants from open strings,”JHEP09(2021) 059,2104.14493

    work page arXiv 2021

  49. [49]

    Higgs Branches of rank-0 5d theories from M- theory on (Aj, Al) and (Ak, Dn) singularities,

    M. De Marco and A. Sangiovanni, “Higgs Branches of rank-0 5d theories from M- theory on (Aj, Al) and (Ak, Dn) singularities,”JHEP03(2022) 099, 2111.05875

    work page arXiv 2022

  50. [50]

    5D and 6D SCFTs fromC3 orbifolds,

    J. Tian and Y.-N. Wang, “5D and 6D SCFTs fromC3 orbifolds,”SciPost Phys. 12(2022), no. 4, 127,2110.15129

    work page arXiv 2022

  51. [51]

    Partition functions and fibering operators on the Coulomb branch of 5d SCFTs,

    C. Closset and H. Magureanu, “Partition functions and fibering operators on the Coulomb branch of 5d SCFTs,”JHEP01(2023) 035,2209.13564

    work page arXiv 2023

  52. [52]

    Flops of any length, Gopakumar-Vafa invariants and 5d Higgs branches,

    A. Collinucci, M. De Marco, A. Sangiovanni, and R. Valandro, “Flops of any length, Gopakumar-Vafa invariants and 5d Higgs branches,”JHEP08(2022) 292, 2204.10366

    work page arXiv 2022

  53. [53]

    5d Higgs branches from M- theory on quasi-homogeneous cDV threefold singularities,

    M. De Marco, A. Sangiovanni, and R. Valandro, “5d Higgs branches from M- theory on quasi-homogeneous cDV threefold singularities,”JHEP10(2022) 124, 2205.01125. 67

    work page arXiv 2022

  54. [54]

    Reading between the rational sections: Global structures of 4d N = 2KK theories,

    C. Closset and H. Magureanu, “Reading between the rational sections: Global structures of 4d N = 2KK theories,”SciPost Phys.16(2024), no. 5, 137, 2308.10225

    work page arXiv 2024

  55. [55]

    5d SCFTs from isolated complete intersec- tion singularities,

    J. Mu, Y.-N. Wang, and H. N. Zhang, “5d SCFTs from isolated complete intersec- tion singularities,”JHEP02(2024) 155,2311.05441

    work page arXiv 2024

  56. [56]

    Generalized Toric Polygons, T-branes, and 5d SCFTs,

    A. Bourget, A. Collinucci, and S. Schafer-Nameki, “Generalized Toric Polygons, T-branes, and 5d SCFTs,”2301.05239

    work page arXiv

  57. [57]

    (−1)-form symmetries from M-theory and SymTFTs,

    M. Najjar, L. Santilli, and Y.-N. Wang, “(−1)-form symmetries from M-theory and SymTFTs,”JHEP03(2025) 134,2411.19683

    work page arXiv 2025

  58. [58]

    From Quivers to Geometry: 5d Conformal Matter

    A. Bourget, M. De Marco, M. Del Zotto, J. F. Grimminger, and A. Sangiovanni, “From Quivers to Geometry: 5d Conformal Matter,”2605.03119

    work page internal anchor Pith review Pith/arXiv arXiv

  59. [59]

    Frozen

    Y. Tachikawa, “Frozen singularities in M and F theory,”JHEP06(2016) 128, 1508.06679

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  60. [60]

    Frozen generalized symmetries,

    M. Cvetič, M. Dierigl, L. Lin, E. Torres, and H. Y. Zhang, “Frozen generalized symmetries,”Phys. Rev. D111(2025), no. 2, 026018,2410.07318

    work page arXiv 2025

  61. [61]

    Fission, Fusion, and 6D RG Flows

    J. J. Heckman, T. Rudelius, and A. Tomasiello, “Fission, Fusion, and 6D RG Flows,”JHEP02(2019) 167,1807.10274

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  62. [62]

    Universal Features of BPS Strings in Six-dimensional SCFTs

    M. Del Zotto and G. Lockhart, “Universal Features of BPS Strings in Six- dimensional SCFTs,”JHEP08(2018) 173,1804.09694

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  63. [63]

    F-theory and the Classification of Little Strings

    L. Bhardwaj, M. Del Zotto, J. J. Heckman, D. R. Morrison, T. Rudelius, and C. Vafa, “F-theory and the Classification of Little Strings,”Phys. Rev. D93(2016), no. 8, 086002,1511.05565. [Erratum: Phys.Rev.D 100, 029901 (2019)]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  64. [64]

    Revisiting the classifications of 6d SCFTs and LSTs,

    L. Bhardwaj, “Revisiting the classifications of 6d SCFTs and LSTs,”JHEP03 (2020) 171,1903.10503

    work page arXiv 2020

  65. [65]

    6d Conformal Matter

    M. Del Zotto, J. J. Heckman, A. Tomasiello, and C. Vafa, “6d Conformal Matter,” JHEP02(2015) 054,1407.6359

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  66. [66]

    Small instanton transitions for M5 fractions

    N. Mekareeya, K. Ohmori, H. Shimizu, and A. Tomasiello, “Small instanton transitions for M5 fractions,”JHEP10(2017) 055,1707.05785

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  67. [67]

    N=2 dualities

    D. Gaiotto, “N=2 dualities,”JHEP08(2012) 034,0904.2715. 68

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  68. [68]

    Wall-crossing, Hitchin Systems, and the WKB Approximation

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

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  69. [69]

    Gaiotto Duality for the Twisted A_{2N-1} Series

    O. Chacaltana, J. Distler, and Y. Tachikawa, “Gaiotto duality for the twisted A2N−1 series,”JHEP05(2015) 075,1212.3952

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  70. [70]

    Tinkertoys for the D_N series

    O. Chacaltana and J. Distler, “Tinkertoys for theDN series,”JHEP02(2013) 110,1106.5410

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  71. [71]

    Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories

    O. Chacaltana, J. Distler, and Y. Tachikawa, “Nilpotent orbits and codimension- two defects of 6d N=(2,0) theories,”Int. J. Mod. Phys. A28(2013) 1340006, 1203.2930

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  72. [72]

    Tinkertoys for the Twisted D-Series,

    O. Chacaltana, J. Distler, and A. Trimm, “Tinkertoys for the Twisted D-Series,” JHEP04(2015) 173,1309.2299

    work page arXiv 2015

  73. [73]

    Tinkertoys for the TwistedE6 Theory,

    O. Chacaltana, J. Distler, and A. Trimm, “Tinkertoys for the TwistedE6 Theory,” 1501.00357

    work page arXiv

  74. [74]

    Tinkertoys for the E7 Theory

    O. Chacaltana, J. Distler, A. Trimm, and Y. Zhu, “Tinkertoys for the E7 theory,” JHEP05(2018) 031,1704.07890

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  75. [75]

    Tinkertoys for the $E_8$ Theory

    O. Chacaltana, J. Distler, A. Trimm, and Y. Zhu, “Tinkertoys for theE8 Theory,” 1802.09626

    work page internal anchor Pith review Pith/arXiv arXiv

  76. [76]

    SCFTs, Holography, and Topological Strings

    H. Hayashi, P. Jefferson, H.-C. Kim, K. Ohmori, and C. Vafa, “SCFTs, holog- raphy, and topological strings,”Surveys Diff. Geom.23(2018), no. 1, 105–211, 1905.00116

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  77. [77]

    Trifectas for TN in 5d,

    J. Eckhard, S. Schäfer-Nameki, and Y.-N. Wang, “Trifectas for TN in 5d,”JHEP 07(2020), no. 07, 199,2004.15007

    work page arXiv 2020

  78. [78]

    Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics

    N. Seiberg, “Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics,”Phys. Lett. B388(1996) 753–760,hep-th/9608111

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  79. [79]

    Extremal Transitions and Five-Dimensional Supersymmetric Field Theories

    D. R. Morrison and N. Seiberg, “Extremal transitions and five-dimensional super- symmetric field theories,”Nucl. Phys. B483(1997) 229–247,hep-th/9609070

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  80. [80]

    Cft’s from calabi–yau four-folds,

    S. Gukov, C. Vafa, and E. Witten, “Cft’s from calabi–yau four-folds,”Nuclear Physics B584(Sep, 2000) 69–108. 69

    work page 2000

Showing first 80 references.