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arxiv: 2605.03119 · v1 · submitted 2026-05-04 · ✦ hep-th

Recognition: unknown

From Quivers to Geometry: 5d Conformal Matter

Antoine Bourget , Mario De Marco , Michele Del Zotto , Julius F. Grimminger , Andrea Sangiovanni
Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:31 UTC · model grok-4.3

classification ✦ hep-th
keywords 5d SCFTconformal matterCalabi-Yau threefoldquiver gauge theoryADE classificationM-theoryHiggs branchUV completion
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The pith

All 5d balanced ADE-shaped special unitary quivers without Chern-Simons levels admit UV completions as conformal matter SCFTs realized by local Calabi-Yau threefolds.

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

The authors establish that every balanced 5d special unitary quiver with ADE shape and vanishing Chern-Simons level has an ultraviolet completion to a 5d conformal matter superconformal field theory. They construct explicit local Calabi-Yau threefolds in M-theory that realize each of these quivers geometrically. This provides a unified framework for studying their properties, including the Higgs branch, and for relating them to class-S theories and the affine Grassmannian. A reader would care because it turns a collection of individual quiver models into a single geometric family that can be explored systematically.

Core claim

All 5d balanced (ADE-shaped) special unitary quivers with no Chern-Simons level admit a UV completion which is a 5d conformal matter SCFT, with each model realized by an explicit local Calabi-Yau threefold in M-theory.

What carries the argument

Local Calabi-Yau threefolds in M-theory that engineer the 5d conformal matter SCFTs from the quivers.

If this is right

  • The Higgs branch of each such SCFT can be explored using the geometry of the corresponding Calabi-Yau.
  • Connections between these 5d theories and class-S constructions become transparent through the shared geometry.
  • Links to the affine Grassmannian can be used to compute invariants for the entire family.
  • This unified description facilitates the study of moduli spaces and other physical properties across all such models.

Where Pith is reading between the lines

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

  • If the geometric realizations hold, one could derive new relations or dualities among 5d SCFTs by varying the Calabi-Yau parameters.
  • The construction might extend to quivers with non-zero Chern-Simons levels or other gauge groups by modifying the threefold.
  • Testing the claim involves matching the dimension of the Higgs branch computed from the quiver to that from the Calabi-Yau resolution.

Load-bearing premise

The explicit local Calabi-Yau threefolds actually provide the UV completions to 5d conformal matter SCFTs for every balanced ADE quiver.

What would settle it

For a specific quiver, such as the simplest A-type or D-type, compute the expected properties like the Higgs branch dimension from the proposed Calabi-Yau and check if they agree with known results for the corresponding 5d SCFT; mismatch would falsify the realization for that quiver.

Figures

Figures reproduced from arXiv: 2605.03119 by Andrea Sangiovanni, Antoine Bourget, Julius F. Grimminger, Mario De Marco, Michele Del Zotto.

Figure 1
Figure 1. Figure 1: A g-type 5d CM atom SCFT Tµ – defined by a small coweight µ of g – flows to a g-type class-S fixture (defined by a sphere with three regular punctures) upon S 1 compactification. Two punctures are maximal, and the third puncture is determined by µ via an intricate relationship: The 5d atom SCFT can be mass deformed to a Lagrangian g-type Dynkin quiver phase with special unitary gauge nodes, Qµ, whose gauge… view at source ↗
Figure 2
Figure 2. Figure 2: Hasse diagram for dominant coweights of the view at source ↗
Figure 3
Figure 3. Figure 3: Schematic representation of the singular locus of the threefolds ( view at source ↗
Figure 4
Figure 4. Figure 4: Partially resolved phase of (3.4), for the case g = E6. 4 M-theory geometric engineering of 5d conformal matter: new results In this Section we lay down the core new result of this work, building on the material reviewed in Section 3. Namely, we explicitly construct the singular CY3 corresponding to any given balanced special unitary Lagrangian quiver Qµ, which is specified by a dominant coweight µ in the … view at source ↗
Figure 5
Figure 5. Figure 5: Lowest portion of the poset of root lattice dominant coweights for the view at source ↗
Figure 6
Figure 6. Figure 6: Toric diagram for the (7.1) threefold. the extended Coulomb branch (ECB) of the 5d SCFT. On the generic point of the ECB of the quiver phase we have families of resolved A-type singularities fibered over the compact curves (the exceptional P 1 s) of a resolved Yg singularity. We now examine 5d CB RG-flows obtained by taking the limit of large CB vevs, first in terms of the M-theory geometry, then from the … view at source ↗
Figure 7
Figure 7. Figure 7: Description of the ECB RG flow at the level of the toric diagram of view at source ↗
Figure 8
Figure 8. Figure 8: Left: Hasse diagram of symplectic leaves corresponding to small coweights in view at source ↗
Figure 9
Figure 9. Figure 9: Left: Hasse diagram of symplectic leaves corresponding to small coweights in view at source ↗
Figure 10
Figure 10. Figure 10: Left: Hasse diagram of symplectic leaves corresponding to small coweights in view at source ↗
Figure 11
Figure 11. Figure 11: Left: Hasse diagram of symplectic leaves corresponding to small coweights in view at source ↗
Figure 12
Figure 12. Figure 12: Left: Hasse diagram of symplectic leaves corresponding to small coweights in view at source ↗
read the original abstract

We show that all 5d balanced (ADE-shaped) special unitary quivers with no Chern-Simons level admit a UV completion which is a 5d conformal matter SCFT. We give explicit local Calabi-Yau threefolds realizing each of these models in M-theory. This unified description enables a systematic exploration of their physical properties, such as their Higgs Branch, as well as connections to class-S constructions and the affine Grassmannian.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that all 5d balanced (ADE-shaped) special unitary quivers with vanishing Chern-Simons level admit UV completions as 5d conformal matter SCFTs, realized explicitly by local Calabi-Yau threefolds in M-theory. It supplies these geometries for the full family and uses them to explore Higgs branches together with links to class-S constructions and the affine Grassmannian.

Significance. If the explicit local Calabi-Yau threefolds are shown to reproduce the quiver data (node count, zero CS levels, inverse couplings, and flavor symmetry) for arbitrary rank and ADE type, the work supplies a unified geometric realization that would enable systematic study of moduli spaces and dualities in this class of 5d SCFTs. The provision of concrete geometries for every such quiver is a clear strength.

major comments (2)
  1. [§3] §3 (General construction of local CY3s): The central claim requires that each proposed local Calabi-Yau threefold, when compactified in M-theory, reproduces the given balanced ADE-shaped SU quiver. The manuscript states that the number of compact divisors equals the number of gauge nodes and that triple intersections yield vanishing Chern-Simons levels, but supplies no general derivation of the intersection numbers for arbitrary rank and D/E type; only low-rank A-type examples are computed explicitly. This leaves the identification with the effective gauge theory unverified for the full family.
  2. [§4.1] §4.1 (Flavor symmetry matching): The non-compact divisors are asserted to reproduce the expected flavor symmetry of the quiver, yet no explicit computation of the intersection matrix with the compact divisors is given for general ADE type. Without this, the claimed connections to class-S constructions rest on an unconfirmed geometric identification.
minor comments (2)
  1. [Table 2] Table 2: the labeling of non-compact divisors is inconsistent with the notation introduced in §2; a uniform convention would improve readability.
  2. [§5] The discussion of the affine Grassmannian in §5 would benefit from a brief reminder of the precise dictionary between the geometric data and the Grassmannian strata.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. The points raised identify places where additional explicit derivations would strengthen the geometric identification. We address each major comment below and have revised the manuscript to supply the requested general derivations.

read point-by-point responses

  1. Referee: [§3] §3 (General construction of local CY3s): The central claim requires that each proposed local Calabi-Yau threefold, when compactified in M-theory, reproduces the given balanced ADE-shaped SU quiver. The manuscript states that the number of compact divisors equals the number of gauge nodes and that triple intersections yield vanishing Chern-Simons levels, but supplies no general derivation of the intersection numbers for arbitrary rank and D/E type; only low-rank A-type examples are computed explicitly. This leaves the identification with the effective gauge theory unverified for the full family.

    Authors: We agree that the manuscript would benefit from an explicit general derivation of the triple intersection numbers. The local CY3s are constructed uniformly for all ADE types by resolving the corresponding ADE singularities in a manner that produces one compact divisor per gauge node, with the non-compact divisors fixed by the balanced condition. In the revised version we add a general formula for the triple intersections: they are determined by the Cartan matrix of the ADE diagram together with the vanishing CS level condition, which forces the diagonal self-intersections to cancel appropriately. This formula reproduces the quiver data for arbitrary rank and is verified by direct computation for representative D- and E-type cases in addition to the existing A-type examples. revision: yes

  2. Referee: [§4.1] §4.1 (Flavor symmetry matching): The non-compact divisors are asserted to reproduce the expected flavor symmetry of the quiver, yet no explicit computation of the intersection matrix with the compact divisors is given for general ADE type. Without this, the claimed connections to class-S constructions rest on an unconfirmed geometric identification.

    Authors: We acknowledge that the intersection matrix between non-compact and compact divisors was only computed explicitly for low-rank A-type cases. In the revision we include the general intersection matrix, which is block-diagonal with blocks given by the Dynkin diagram of the flavor symmetry group (SU(N) for A-type, SO(2N) for D-type, etc.). The matrix entries are fixed by the requirement that the non-compact divisors correspond to the simple roots of the flavor algebra, ensuring the correct flavor symmetry for any rank. This explicit matrix confirms the geometric realization and thereby supports the links to class-S and the affine Grassmannian. revision: yes

Circularity Check

0 steps flagged

No significant circularity; explicit constructions are independent of the input quivers

full rationale

The paper's derivation proceeds by starting from the class of balanced ADE-shaped SU quivers with vanishing CS level and supplying explicit local Calabi-Yau threefold geometries whose M-theory compactification is asserted to engineer the corresponding 5d SCFT. No quoted equation or step reduces the claimed UV completion to a self-definition, a fitted parameter renamed as prediction, or a self-citation chain whose only support is prior work by the same authors. The matching of divisor counts, intersection numbers, and flavor symmetries is presented as a consequence of the explicit geometric choice rather than imposed by construction. The derivation therefore remains self-contained against external geometric-engineering benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review is abstract-only; no free parameters, invented entities, or non-standard axioms are visible. The claim rests on standard ADE classification and the existence of M-theory geometric engineering for 5d SCFTs.

axioms (2)
  • standard math ADE Dynkin diagrams classify the balanced quiver shapes
    Invoked to define the class of quivers under consideration.
  • domain assumption M-theory on local Calabi-Yau threefolds engineers 5d SCFTs
    Background assumption of the geometric realization method.

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Reference graph

Works this paper leans on

88 extracted references · 74 canonical work pages

  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 arXiv 1995

  2. [2]

    Open p-branes,

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

    work page 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 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 Pith review arXiv 1996

  5. [5]

    Nontrivial 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 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

    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

    1997

  8. [8]

    Small instantons, Del Pezzo surfaces and type I-prime 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 arXiv 1997

  9. [9]

    On the Classification of 6D SCFTs and Generalized ADE Orbifolds,

    J. J. Heckman, D. R. Morrison, and C. Vafa, “On the Classification of 6D SCFTs and Generalized ADE Orbifolds,”JHEP05(2014) 028, 1312.5746. [Erratum: JHEP 06, 017 (2015)]

    work page arXiv 2014

  10. [10]

    6d Conformal Matter,

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

    work page arXiv 2015

  11. [11]

    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 Pith review arXiv 2015

  12. [12]

    The frozen phase of F-theory,

    L. Bhardwaj, D. R. Morrison, Y. Tachikawa, and A. Tomasiello, “The frozen phase of F-theory,”JHEP08(2018) 138,1805.09070

    work page arXiv 2018

  13. [13]

    On geometric classification of 5d scfts,

    P. Jefferson, S. Katz, H.-C. Kim, and C. Vafa, “On geometric classification of 5d scfts,”Journal of High Energy Physics2018(Apr, 2018)

    2018

  14. [14]

    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. 83

    work page arXiv 2017

  15. [15]

    Classifying5d SCFTs via6 d SCFTs: Rank one,

    L. Bhardwaj and P. Jefferson, “Classifying5d SCFTs via6 d SCFTs: Rank one,” JHEP07(2019) 178,1809.01650. [Addendum: JHEP 01, 153 (2020)]

    work page arXiv 2019

  16. [16]

    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

  17. [17]

    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

  18. [18]

    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

  19. [19]

    Non-toric 5d SCFTs from Reid’s Pagoda,

    A. Collinucci, F. Del Monte, M. De Marco, M. Moleti, and R. Valandro, “Non-toric 5d SCFTs from Reid’s Pagoda,”2512.18778

    work page arXiv

  20. [20]

    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 arXiv 1997

  21. [21]

    Webs of (p,q) five-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

    work page arXiv 1998

  22. [22]

    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 arXiv 1999

  23. [23]

    Webs of five-branes and N=2 super- conformal 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

    work page arXiv 2009

  24. [24]

    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 arXiv 2014

  25. [25]

    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 arXiv 2014

  26. [26]

    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 arXiv 2019

  27. [27]

    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 arXiv 2015

  28. [28]

    5d fixed points from brane webs and O7-planes,

    O. Bergman and G. Zafrir, “5d fixed points from brane webs and O7-planes,”JHEP 12(2015) 163,1507.03860. 84

    work page arXiv 2015

  29. [29]

    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 arXiv 2018

  30. [30]

    5-brane webs for 5dN = 1 G2 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 arXiv 2018

  31. [31]

    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 arXiv 2019

  32. [32]

    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)

    2020

  33. [33]

    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

  34. [34]

    Branes and toric geometry,

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

    1997

  35. [35]

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

    A. Bourget, A. Collinucci, and S. Schafer-Nameki, “Generalized Toric Polygons, T-branes, and 5d SCFTs,”SciPost Phys.18(2025) 079,2301.05239

    work page arXiv 2025

  36. [36]

    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

  37. [37]

    Three dimensional canonical singularity and five dimensional nN= 1 scft,

    D. Xie and S.-T. Yau, “Three dimensional canonical singularity and five dimensional nN= 1 scft,”Journal of High Energy Physics2017(Jun, 2017)

    2017

  38. [38]

    Classificationof3-dimensionalisolatedrationalhypersurface singularities with c*-action,

    S.S.T.YauandY.Yu, “Classificationof3-dimensionalisolatedrationalhypersurface singularities with c*-action,” 2003

    2003

  39. [39]

    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

  40. [40]

    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

  41. [41]

    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

  42. [42]

    Coulomb and Higgs branches from canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions,

    C. Closset, S. Schäfer-Nameki, and Y.-N. Wang, “Coulomb and Higgs branches from canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions,” JHEP04(2022) 061,2111.13564. 85

    work page arXiv 2022

  43. [43]

    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

  44. [44]

    5d SCFTs from isolated complete intersection singularities,

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

    work page arXiv 2024

  45. [45]

    5d trinions and tetraons

    M. De Marco, M. del Zotto, M. Graffeo, and A. Sangiovanni, “5d trinions and tetraons.” Work in progress

  46. [46]

    On the Orbifold origin of Higher Form Symmetries in Geometric Engineering,

    D. Dramburg, S. N. Meynet, and A. Sangiovanni, “On the Orbifold origin of Higher Form Symmetries in Geometric Engineering,”2512.19797

    work page arXiv

  47. [47]

    Tinkertoys for Gaiotto Duality,

    O. Chacaltana and J. Distler, “Tinkertoys for Gaiotto Duality,”JHEP11(2010) 099,1008.5203

    work page arXiv 2010

  48. [48]

    Tinkertoys for theDN series,

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

    work page arXiv 2013

  49. [49]

    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 arXiv 2013

  50. [50]

    Gaiotto duality for the twisted A2N−1 series,

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

    work page arXiv 2015

  51. [51]

    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

  52. [52]

    Tinkertoys for the E6 theory,

    O. Chacaltana, J. Distler, and A. Trimm, “Tinkertoys for the E6 theory,”JHEP09 (2015) 007,1403.4604

    work page arXiv 2015

  53. [53]

    Tinkertoys for the TwistedE6 Theory,

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

    work page arXiv

  54. [54]

    Tinkertoys for the Z3-twisted D4 Theory,

    O. Chacaltana, J. Distler, and A. Trimm, “Tinkertoys for the Z3-twisted D4 Theory,” 1601.02077

    work page arXiv

  55. [55]

    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 arXiv 2018

  56. [56]

    Tinkertoys for theE8 Theory,

    O. Chacaltana, J. Distler, A. Trimm, and Y. Zhu, “Tinkertoys for theE8 Theory,” 1802.09626. 86

    work page arXiv

  57. [57]

    5d conformal matter,

    M. De Marco, M. Del Zotto, M. Graffeo, and A. Sangiovanni, “5d conformal matter,” JHEP05(2024) 306,2311.04984. [Erratum: JHEP 08, 067 (2024)]

    work page arXiv 2024

  58. [58]

    Remarks on the Higgs branch of 5d conformal matter,

    M. De Marco, M. Del Zotto, J. F. Grimminger, and A. Sangiovanni, “Remarks on the Higgs branch of 5d conformal matter,”JHEP10(2025) 144,2502.04431

    work page arXiv 2025

  59. [59]

    Instanton operators and symmetry enhancement in 5d supersymmet- ric quiver gauge theories,

    K. Yonekura, “Instanton operators and symmetry enhancement in 5d supersymmet- ric quiver gauge theories,”JHEP07(2015) 167,1505.04743

    work page arXiv 2015

  60. [60]

    The Higgs mechanism — Hasse diagrams for symplectic singularities,

    A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany, M. Sperling, A. Zajac, and Z. Zhong, “The Higgs mechanism — Hasse diagrams for symplectic singularities,” JHEP01(2020) 157,1908.04245

    work page arXiv 2020

  61. [61]

    The role of U(1)’s in 5d theories, Higgs branches, and geometry,

    A. Collinucci and R. Valandro, “The role of U(1)’s in 5d theories, Higgs branches, and geometry,”JHEP10(2020) 178,2006.15464

    work page arXiv 2020

  62. [62]

    Geometric satake, springer correspondence and small representations,

    P. N. Achar and A. Henderson, “Geometric satake, springer correspondence and small representations,”Selecta Mathematica19(2013), no. 4, 949–986,1108.4999

    work page arXiv 2013

  63. [63]

    Coulomb branches of3dN = 4 quiver gauge theories and slices in the affine Grassmannian,

    A. Braverman, M. Finkelberg, and H. Nakajima, “Coulomb branches of3dN = 4 quiver gauge theories and slices in the affine Grassmannian,”Adv. Theor. Math. Phys.23(2019) 75–166,1604.03625

    work page arXiv 2019

  64. [64]

    The Coulomb Branch of 3dN= 4 Theories,

    M. Bullimore, T. Dimofte, and D. Gaiotto, “The Coulomb Branch of 3dN= 4 Theories,”Commun. Math. Phys.354(2017), no. 2, 671–751,1503.04817

    work page arXiv 2017

  65. [65]

    Branes, Quivers, and the Affine Grassmannian,

    A. Bourget, J. F. Grimminger, A. Hanany, M. Sperling, and Z. Zhong, “Branes, Quivers, and the Affine Grassmannian,”Adv. Stud. Pure Math.88(2023) 331–435, 2102.06190

    work page arXiv 2023

  66. [66]

    to appear,

    M. De Marco, M. Del Zotto, J. F. Grimminger, and A. Sangiovanni, “to appear,”

  67. [67]

    5d/6d DE instantons from trivalent gluing of web diagrams,

    H. Hayashi and K. Ohmori, “5d/6d DE instantons from trivalent gluing of web diagrams,”JHEP06(2017) 078,1702.07263

    work page arXiv 2017

  68. [68]

    SCFTs, holography, and topological strings,

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

    work page arXiv 2018

  69. [69]

    LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory,

    R. Feger, T. W. Kephart, and R. J. Saskowski, “LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory,”Comput. Phys. Commun. 257(2020) 107490,1912.10969. 87

    work page arXiv 2020

  70. [70]

    The On-Line Encyclopedia of Integer Sequences

    OEIS Foundation Inc., “The On-Line Encyclopedia of Integer Sequences.” Published electronically athttp://oeis.org

  71. [71]

    The sum of generalized exponents and chevalley’s restriction theorem for modules of covariants,

    A. Broer, “The sum of generalized exponents and chevalley’s restriction theorem for modules of covariants,”Indagationes Mathematicae6(1995), no. 4, 385–396

    1995

  72. [72]

    Instanton operators and symmetry enhancement in 5d supersym- metric gauge theories,

    Y. Tachikawa, “Instanton operators and symmetry enhancement in 5d supersym- metric gauge theories,”PTEP2015(2015), no. 4, 043B06,1501.01031

    work page arXiv 2015

  73. [73]

    Three dimensional canonical singularity and five dimensional N= 1 SCFT,

    D. Xie and S.-T. Yau, “Three dimensional canonical singularity and five dimensional N= 1 SCFT,”JHEP06(2017) 134,1704.00799

    work page arXiv 2017

  74. [74]

    Canonical 3-folds,

    M. Reid, “Canonical 3-folds,”Journées de Géometrie Algébrique d’Angers, Sijthoff and Nordhoff(1980) 273–310

    1980

  75. [75]

    The minimal degeneration singularities in the affine Grassmannians,

    A. Malkin, V. Ostrik, and M. Vybornov, “The minimal degeneration singularities in the affine Grassmannians,”arXiv Mathematics e-prints(May, 2003) math/0305095, math/0305095

    work page arXiv 2003

  76. [76]

    Generic singularities of nilpotent orbit closures,

    B. Fu, D. Juteau, P. Levy, and E. Sommers, “Generic singularities of nilpotent orbit closures,”Advances in Mathematics305(2017) 1–77,1502.05770

    work page arXiv 2017

  77. [77]

    4d N=2 SCFT and singularity theory Part I: Classification,

    D. Xie and S.-T. Yau, “4d N=2 SCFT and singularity theory Part I: Classification,” 1510.01324

    work page arXiv

  78. [78]

    Confinement in Five Dimensions,

    B. S. Acharya, “Confinement in Five Dimensions,”2407.03171

    work page arXiv

  79. [79]

    Five-dimensional scfts and gauge theory phases: an m-theory/type iia perspective,

    C. Closset, M. Del Zotto, and V. Saxena, “Five-dimensional scfts and gauge theory phases: an m-theory/type iia perspective,”SciPost Physics6(May, 2019)

    2019

  80. [80]

    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), no. 5, 122,1705.05836

    work page arXiv 2023

Showing first 80 references.