Built on

L. Bhardwaj, Revisiting the classifications of 6d SCFTs and LSTs , JHEP 03
Original
1903
Earlier work this paper cites.
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, 5d Superconformal Field Theories and Graphs , Phys. Lett. B 800
Original
1906
Earlier work this paper cites.
F. Apruzzi, C. Lawrie, L. Lin, S. Schafer-Nameki and Y.-N. Wang, Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States , JHEP 11
Original
1907
Earlier work this paper cites.
A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany, M. Sperling, A. Zajac et al., The Higgs mechanism — Hasse diagrams for symplectic singularities , JHEP 01
Original
1908
Earlier work this paper cites.
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities , JHEP 03
Original
1909
Earlier work this paper cites.
L. Bhardwaj, On the classification of 5d SCFTs , JHEP 09
Original
1909
Earlier work this paper cites.
L. Bhardwaj, Dualities of 5d gauge theories from S-duality , JHEP 07
Original
1909
Earlier work this paper cites.
L. Bhardwaj, P. Jefferson, H.-C. Kim, H.-C. Tarazi and C. Vafa, Twisted Circle Compactifications of 6d SCFTs , JHEP 12
Original
1909
Earlier work this paper cites.
V. Saxena, Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study , JHEP 04
Original
1911
Earlier work this paper cites.
F. Apruzzi, S. Schafer-Nameki and Y.-N. Wang, 5d SCFTs from Decoupling and Gluing , JHEP 08
Original
1912
Earlier work this paper cites.
L. Bhardwaj, Do all 5d SCFTs descend from 6d SCFTs? , JHEP 04
Original
1912
Earlier work this paper cites.
C. Closset and M. Del Zotto, On 5d SCFTs and their BPS quivers. Part I: B-branes and brane tilings , 1912.13502
Original
1912
Earlier work this paper cites.
John Wiley & Sons, Incorporated, 1916, https://doi.org/10.1038/098225b0
G. A. Miller, H. F. Blichfeldt and I. Dickson, Theory and Applications of Finite Groups · 1916
Earlier work this paper cites.
W. M. Fairbairn, T. Fulton and W. H. Klink, Finite and Disconnected Subgroups of SU3 and their Application to the Elementary-Particle Spectrum , J. Math. Phys. 5
1964
Earlier work this paper cites.
V. I. Danilov, The geometry of toric varieties , Russian Mathematical Surveys 33
1978
Earlier work this paper cites.
A. Bovier, M. Lüling and D. Wyler, Finite subgroups of su (3) , Journal of Mathematical Physics 22
1981
Earlier work this paper cites.
W. Fairbairn and T. Fulton, Some comments on finite subgroups of su (3) , Journal of Mathematical Physics 23
1982
Earlier work this paper cites.
K.-i. Watanabe and D. Rotillon, Invariant subrings of ℂ ⁡ [ x , y , z ] \mathbb{C}[x,y,z] which are complete intersections , manuscripta mathematica 39
1982
Earlier work this paper cites.
American Mathematical Soc., 1993, 10.1090/memo/0505
S.-T. Yau, S. S.-T. Yau and Y. Yu, Gorenstein quotient singularities in dimension three , vol. 505 · 1993
Earlier work this paper cites.
No. 131. Princeton University Press, 1993, https://doi.org/10.1515/9781400882526
W. Fulton, Introduction to toric varieties · 1993
Earlier work this paper cites.
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics , Phys. Lett. B388
1996
Earlier work this paper cites.
D. R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories , Nucl. Phys. B483
1997
Earlier work this paper cites.
K. A. Intriligator, D. R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces , Nucl. Phys. B497
1997
Earlier work this paper cites.
O. Aharony and A. Hanany, Branes, superpotentials and superconformal fixed points , Nucl. Phys. B504
1997
Earlier work this paper cites.
D. Markushevich, Resolution of c 3 / h 168 c^{3}/h_{168} , Mathematische Annalen 308
1997
Earlier work this paper cites.
O. Aharony, A. Hanany and B. Kol, Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams , JHEP 01
1998
Earlier work this paper cites.
A. Hanany and A. M. Uranga, Brane boxes and branes on singularities , JHEP 05
1998
Earlier work this paper cites.
O. DeWolfe, A. Hanany, A. Iqbal and E. Katz, Five-branes, seven-branes and five-dimensional E(n) field theories , JHEP 03
1999
Earlier work this paper cites.
A. Hanany and Y.-H. He, NonAbelian finite gauge theories , JHEP 02
1999
Earlier work this paper cites.
T. Muto, D-branes on three-dimensional nonAbelian orbifolds , JHEP 02
1999
Earlier work this paper cites.
B. Feng, A. Hanany and Y.-H. He, The Z(k) x D(k-prime) brane box model , JHEP 09
1999
Earlier work this paper cites.
PhD thesis, Ph. D. thesis, University of Warwick, 1999
M. Caibar, Minimal models of canonical singularities and their cohomology · 1999
Earlier work this paper cites.

Similar

P. S. Aspinwall, S. H. Katz and D. R. Morrison, Lie groups, Calabi-Yau threefolds, and F theory , Adv. Theor. Math. Phys. 4
2000
Cited alongside, same era.
Y. Ito and H. Nakajima, Mckay correspondence and hilbert schemes in dimension three , Topology 39
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Cited alongside, same era.
B. Feng, A. Hanany and Y.-H. He, D-brane gauge theories from toric singularities and toric duality , Nucl. Phys. B 595
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2001
Cited alongside, same era.
L. Bhardwaj and G. Zafrir, Classification of 5d 𝒩 \mathcal{N} = 1 gauge theories , JHEP 12
Original
2003
Cited alongside, same era.

Then

C. Lawrie and S. Schafer-Nameki, The Tate Form on Steroids: Resolution and Higher Codimension Fibers , JHEP 04
Original
2013
Later among the works it cites.
X. L. Hu, N. Jing and W. X. Cai, Generalized mckay quivers of rank three , Acta Mathematica Sinica, English Series 29
2013
Later among the works it cites.
O. Bergman, D. Rodríguez-Gómez and G. Zafrir, 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory , JHEP 03
Original
2014
Later among the works it cites.
G. Zafrir, Duality and enhancement of symmetry in 5d gauge theories , JHEP 12
Original
2014
Later among the works it cites.
C. Hagedorn, A. Meroni and L. Vitale, Mixing patterns from the groups Σ ⁡ ( n ϕ ) \Sigma(n\phi) , J. Phys. A 47
Original

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2021

5D and 6D SCFTs from $\mathbb{C}^3$ orbifolds

Tian, Jiahua, Wang, Yi-Nan

Understand

We study the orbifold singularities $X=\mathbb{C}^3/\Gamma$ where $\Gamma$ is a finite subgroup of $SU(3)$.

M-theory on this orbifold singularity gives rise to a 5d SCFT, which is investigated with two methods.
The first approach is via 3d McKay correspondence which relates the group theoretic data of $\Gamma$ to the physical properties of the 5d SCFT.
In particular, the 1-form symmetry of the 5d SCFT is read off from the McKay quiver of $\Gamma$ in an elegant way.

Built on

L. Bhardwaj, Revisiting the classifications of 6d SCFTs and LSTs , JHEP 03
Original
1903
Earlier work this paper cites.
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, 5d Superconformal Field Theories and Graphs , Phys. Lett. B 800
Original
1906
Earlier work this paper cites.
F. Apruzzi, C. Lawrie, L. Lin, S. Schafer-Nameki and Y.-N. Wang, Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States , JHEP 11
Original
1907
Earlier work this paper cites.
A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany, M. Sperling, A. Zajac et al., The Higgs mechanism — Hasse diagrams for symplectic singularities , JHEP 01
Original
1908
Earlier work this paper cites.
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities , JHEP 03
Original
1909
Earlier work this paper cites.
L. Bhardwaj, On the classification of 5d SCFTs , JHEP 09
Original
1909
Earlier work this paper cites.
L. Bhardwaj, Dualities of 5d gauge theories from S-duality , JHEP 07
Original
1909
Earlier work this paper cites.
L. Bhardwaj, P. Jefferson, H.-C. Kim, H.-C. Tarazi and C. Vafa, Twisted Circle Compactifications of 6d SCFTs , JHEP 12
Original
1909
Earlier work this paper cites.
V. Saxena, Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study , JHEP 04
Original
1911
Earlier work this paper cites.
F. Apruzzi, S. Schafer-Nameki and Y.-N. Wang, 5d SCFTs from Decoupling and Gluing , JHEP 08
Original
1912
Earlier work this paper cites.
L. Bhardwaj, Do all 5d SCFTs descend from 6d SCFTs? , JHEP 04
Original
1912
Earlier work this paper cites.
C. Closset and M. Del Zotto, On 5d SCFTs and their BPS quivers. Part I: B-branes and brane tilings , 1912.13502
Original
1912
Earlier work this paper cites.
John Wiley & Sons, Incorporated, 1916, https://doi.org/10.1038/098225b0
G. A. Miller, H. F. Blichfeldt and I. Dickson, Theory and Applications of Finite Groups · 1916
Earlier work this paper cites.
W. M. Fairbairn, T. Fulton and W. H. Klink, Finite and Disconnected Subgroups of SU3 and their Application to the Elementary-Particle Spectrum , J. Math. Phys. 5
1964
Earlier work this paper cites.
V. I. Danilov, The geometry of toric varieties , Russian Mathematical Surveys 33
1978
Earlier work this paper cites.
A. Bovier, M. Lüling and D. Wyler, Finite subgroups of su (3) , Journal of Mathematical Physics 22
1981
Earlier work this paper cites.
W. Fairbairn and T. Fulton, Some comments on finite subgroups of su (3) , Journal of Mathematical Physics 23
1982
Earlier work this paper cites.
K.-i. Watanabe and D. Rotillon, Invariant subrings of ℂ ⁡ [ x , y , z ] \mathbb{C}[x,y,z] which are complete intersections , manuscripta mathematica 39
1982
Earlier work this paper cites.
American Mathematical Soc., 1993, 10.1090/memo/0505
S.-T. Yau, S. S.-T. Yau and Y. Yu, Gorenstein quotient singularities in dimension three , vol. 505 · 1993
Earlier work this paper cites.
No. 131. Princeton University Press, 1993, https://doi.org/10.1515/9781400882526
W. Fulton, Introduction to toric varieties · 1993
Earlier work this paper cites.
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics , Phys. Lett. B388
1996
Earlier work this paper cites.
D. R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories , Nucl. Phys. B483
1997
Earlier work this paper cites.
K. A. Intriligator, D. R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces , Nucl. Phys. B497
1997
Earlier work this paper cites.
O. Aharony and A. Hanany, Branes, superpotentials and superconformal fixed points , Nucl. Phys. B504
1997
Earlier work this paper cites.
D. Markushevich, Resolution of c 3 / h 168 c^{3}/h_{168} , Mathematische Annalen 308
1997
Earlier work this paper cites.
O. Aharony, A. Hanany and B. Kol, Webs of (p,q) five-branes, five-dimensional field theories and grid diagrams , JHEP 01
1998
Earlier work this paper cites.
A. Hanany and A. M. Uranga, Brane boxes and branes on singularities , JHEP 05
1998
Earlier work this paper cites.
O. DeWolfe, A. Hanany, A. Iqbal and E. Katz, Five-branes, seven-branes and five-dimensional E(n) field theories , JHEP 03
1999
Earlier work this paper cites.
A. Hanany and Y.-H. He, NonAbelian finite gauge theories , JHEP 02
1999
Earlier work this paper cites.
T. Muto, D-branes on three-dimensional nonAbelian orbifolds , JHEP 02
1999
Earlier work this paper cites.
B. Feng, A. Hanany and Y.-H. He, The Z(k) x D(k-prime) brane box model , JHEP 09
1999
Earlier work this paper cites.
PhD thesis, Ph. D. thesis, University of Warwick, 1999
M. Caibar, Minimal models of canonical singularities and their cohomology · 1999
Earlier work this paper cites.

Similar

P. S. Aspinwall, S. H. Katz and D. R. Morrison, Lie groups, Calabi-Yau threefolds, and F theory , Adv. Theor. Math. Phys. 4
2000
Cited alongside, same era.
Y. Ito and H. Nakajima, Mckay correspondence and hilbert schemes in dimension three , Topology 39
2000
Cited alongside, same era.
B. Feng, A. Hanany and Y.-H. He, D-brane gauge theories from toric singularities and toric duality , Nucl. Phys. B 595
2001
Cited alongside, same era.
T. Bridgeland, A. King and M. Reid, The McKay correspondence as an equivalence of derived categories , J. Am. Math. Soc. 14
2001
Cited alongside, same era.
L. Bhardwaj and G. Zafrir, Classification of 5d 𝒩 \mathcal{N} = 1 gauge theories , JHEP 12
Original
2003
Cited alongside, same era.

Then

C. Lawrie and S. Schafer-Nameki, The Tate Form on Steroids: Resolution and Higher Codimension Fibers , JHEP 04
Original
2013
Later among the works it cites.
X. L. Hu, N. Jing and W. X. Cai, Generalized mckay quivers of rank three , Acta Mathematica Sinica, English Series 29
2013
Later among the works it cites.
O. Bergman, D. Rodríguez-Gómez and G. Zafrir, 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory , JHEP 03
Original
2014
Later among the works it cites.
G. Zafrir, Duality and enhancement of symmetry in 5d gauge theories , JHEP 12
Original
2014
Later among the works it cites.
C. Hagedorn, A. Meroni and L. Vitale, Mixing patterns from the groups Σ ⁡ ( n ϕ ) \Sigma(n\phi) , J. Phys. A 47
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

J. Eckhard, S. Schäfer-Nameki and Y.-N. Wang, Trifectas for T N

Original

2004

Cited alongside, same era.

A. Bourget, J. F. Grimminger, A. Hanany, M. Sperling and Z. Zhong, Magnetic Quivers from Brane Webs with O5 Planes , JHEP 07

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L. Bhardwaj, More 5d KK theories , 2005.01722

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2005

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M. Hubner, 5d SCFTs from (E n

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2006

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2014

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J. Serrano, Finite subgroups of sl (2, c) and sl (3, c) , Notes, Warwick (2014) , [ https://homepages.warwick.ac.uk/~masda/McKay/Carrasco_Project.pdf ]

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Later among the works it cites.

J. J. Heckman, D. R. Morrison and C. Vafa, On the Classification of 6D SCFTs and Generalized ADE Orbifolds , JHEP 05

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F. Butin and G. S. Perets, Branching law for finite subgroups of sl(3,c) and mckay correspondence , Journal of Group Theory 17

2014

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G. Zafrir, Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories , JHEP 07

Original

2015