Abstract
We determine 5d \( \mathcal{N} \) = 1 SCFTs originating from 6d (En, Em) conformal matter theories with n ≠ m by circle reduction and mass deformations. The marginal geometries are constructed and we derive their combined fiber diagrams (CFDs). The CFDs allow for an enumeration of descendant SCFTs obtained by decoupling matter hypermultiplets and a description of candidate weakly coupled quivers.
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N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
K.A. Intriligator, D.R. Morrison and N. Seiberg, Five-dimensional supersymmetric gauge theories and degenerations of Calabi-Yau spaces, Nucl. Phys. B 497 (1997) 56 [hep-th/9702198] [INSPIRE].
D.R. Morrison and N. Seiberg, Extremal transitions and five-dimensional supersymmetric field theories, Nucl. Phys. B 483 (1997) 229 [hep-th/9609070] [INSPIRE].
M. Del Zotto, J.J. Heckman and D.R. Morrison, 6D SCFTs and phases of 5D theories, JHEP 09 (2017) 147 [arXiv:1703.02981] [INSPIRE].
D. Xie and S.-T. Yau, Three dimensional canonical singularity and five dimensional \( \mathcal{N} \) = 1 SCFT, JHEP 06 (2017) 134 [arXiv:1704.00799] [INSPIRE].
J. Tian and Y.-N. Wang, E-string spectrum and typical F-theory geometry, arXiv:1811.02837 [INSPIRE].
L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank, JHEP 10 (2019) 282 [arXiv:1811.10616] [INSPIRE].
L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: Rank one, JHEP 07 (2019) 178 [Addendum ibid. 01 (2020) 153] [arXiv:1809.01650] [INSPIRE].
P. Jefferson, S. Katz, H.-C. Kim and C. Vafa, On geometric classification of 5d SCFTs, JHEP 04 (2018) 103 [arXiv:1801.04036] [INSPIRE].
F. Apruzzi, L. Lin and C. Mayrhofer, Phases of 5d SCFTs from M-/F-theory on non-flat fibrations, JHEP 05 (2019) 187 [arXiv:1811.12400] [INSPIRE].
C. Closset, M. Del Zotto and V. Saxena, Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective, SciPost Phys. 6 (2019) 052 [arXiv:1812.10451] [INSPIRE].
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.N. Wang, 5d superconformal field theories and graphs, Phys. Lett. B 800 (2020) 135077 [arXiv:1906.11820].
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, JHEP 11 (2019) 068 [arXiv:1907.05404] [INSPIRE].
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 (2020) 052 [arXiv:1909.09128] [INSPIRE].
F. Apruzzi, S. Schäfer-Nameki and Y.-N. Wang, 5d SCFTs from decoupling and gluing, JHEP 08 (2020) 153 [arXiv:1912.04264] [INSPIRE].
L. Bhardwaj, Dualities of 5d gauge theories from S-duality, JHEP 07 (2020) 012 [arXiv:1909.05250] [INSPIRE].
L. Bhardwaj, P. Jefferson, H.-C. Kim, H.-C. Tarazi and C. Vafa, Twisted circle compactifications of 6d SCFTs, arXiv:1909.11666 [INSPIRE].
V. Saxena, Rank-two 5d SCFTs from M-theory at isolated toric singularities: a systematic study, JHEP 04 (2020) 198 [arXiv:1911.09574] [INSPIRE].
C. Closset and M. Del Zotto, On 5d SCFTs and their BPS quivers. Part I: B-branes and brane tilings, arXiv:1912.13502 [INSPIRE].
L. Bhardwaj and G. Zafrir, Classification of 5d N = 1 gauge theories, arXiv:2003.04333 [INSPIRE].
P. Corvilain, 6d \( \mathcal{N} \) = (1, 0) anomalies on S1 and F-theory implications, JHEP 08 (2020) 133 [arXiv:2005.12935] [INSPIRE].
D.R. Morrison, S. Schäfer-Nameki and B. Willett, Higher-form symmetries in 5d, JHEP 09 (2020) 024 [arXiv:2005.12296] [INSPIRE].
F. Albertini, M. Del Zotto, I. García Etxebarria and S.S. Hosseini, Higher form symmetries and M-theory, arXiv:2005.12831 [INSPIRE].
J.J. Heckman, D.R. Morrison and C. Vafa, On the classification of 6D SCFTs and generalized ADE orbifolds, JHEP 05 (2014) 028 [Erratum ibid. 06 (2015) 017] [arXiv:1312.5746] [INSPIRE].
J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, Atomic classification of 6D SCFTs, Fortsch. Phys. 63 (2015) 468 [arXiv:1502.05405] [INSPIRE].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d conformal matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
J.J. Heckman, T. Rudelius and A. Tomasiello, Fission, fusion, and 6D RG flows, JHEP 02 (2019) 167 [arXiv:1807.10274] [INSPIRE].
G. Ferlito, A. Hanany, N. Mekareeya and G. Zafrir, 3d Coulomb branch and 5d Higgs branch at infinite coupling, JHEP 07 (2018) 061 [arXiv:1712.06604] [INSPIRE].
S. Cabrera, A. Hanany and F. Yagi, Tropical geometry and five dimensional Higgs branches at infinite coupling, JHEP 01 (2019) 068 [arXiv:1810.01379] [INSPIRE].
S. Cabrera and A. Hanany, Quiver subtractions, JHEP 09 (2018) 008 [arXiv:1803.11205] [INSPIRE].
S. Cabrera, A. Hanany and A. Zajac, Minimally unbalanced quivers, JHEP 02 (2019) 180 [arXiv:1810.01495] [INSPIRE].
A. Bourget, S. Cabrera, J.F. Grimminger, A. Hanany and Z. Zhong, Brane webs and magnetic quivers for SQCD, JHEP 03 (2020) 176 [arXiv:1909.00667] [INSPIRE].
A. Bourget et al., The Higgs mechanism — Hasse diagrams for symplectic singularities, JHEP 01 (2020) 157 [arXiv:1908.04245] [INSPIRE].
J. Eckhard, S. Schäfer-Nameki and Y.-N. Wang, Trifectas for TN in 5d, JHEP 07 (2020) 199 [arXiv:2004.15007] [INSPIRE].
A. Bourget, J.F. Grimminger, A. Hanany, M. Sperling and Z. Zhong, Magnetic quivers from brane webs with O5 planes, JHEP 07 (2020) 204 [arXiv:2004.04082] [INSPIRE].
O. Aharony and A. Hanany, Branes, superpotentials and superconformal fixed points, Nucl. Phys. B 504 (1997) 239 [hep-th/9704170] [INSPIRE].
H.-C. Kim, S.-S. Kim and K. Lee, 5-dim superconformal index with enhanced En global symmetry, JHEP 10 (2012) 142 [arXiv:1206.6781] [INSPIRE].
Y. Tachikawa, Instanton operators and symmetry enhancement in 5d supersymmetric gauge theories, PTEP 2015 (2015) 043B06 [arXiv:1501.01031] [INSPIRE].
G. Zafrir, Duality and enhancement of symmetry in 5d gauge theories, JHEP 12 (2014) 116 [arXiv:1408.4040] [INSPIRE].
O. Bergman, D. Rodríguez-Gómez and G. Zafrir, 5-brane webs, symmetry enhancement, and duality in 5d supersymmetric gauge theory, JHEP 03 (2014) 112 [arXiv:1311.4199] [INSPIRE].
V. Mitev, E. Pomoni, M. Taki and F. Yagi, Fiber-base duality and global symmetry enhancement, JHEP 04 (2015) 052 [arXiv:1411.2450] [INSPIRE].
K. Yonekura, Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories, JHEP 07 (2015) 167 [arXiv:1505.04743] [INSPIRE].
C. Hwang, J. Kim, S. Kim and J. Park, General instanton counting and 5d SCFT, JHEP 07 (2015) 063 [Addendum ibid. 04 (2016) 094] [arXiv:1406.6793] [INSPIRE].
G. Zafrir, Instanton operators and symmetry enhancement in 5d supersymmetric USp, SO and exceptional gauge theories, JHEP 07 (2015) 087 [arXiv:1503.08136] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Dualities and 5-brane webs for 5d rank 2 SCFTs, JHEP 12 (2018) 016 [arXiv:1806.10569] [INSPIRE].
C.F. Uhlemann, Exact results for 5d SCFTs of long quiver type, JHEP 11 (2019) 072 [arXiv:1909.01369] [INSPIRE].
P. Jefferson, H.-C. Kim, C. Vafa and G. Zafrir, Towards classification of 5d SCFTs: single gauge node, arXiv:1705.05836 [INSPIRE].
S. Ferrara, R.R. Khuri and R. Minasian, M theory on a Calabi-Yau manifold, Phys. Lett. B 375 (1996) 81 [hep-th/9602102] [INSPIRE].
J. Tate, Algorithm for determining the type of a singular fiber in an elliptic pencil, Lecture Notes in Mathematics volume 476, Springer, Germany (1975).
M. Bershadsky, K.A. Intriligator, S. Kachru, D.R. Morrison, V. Sadov and C. Vafa, Geometric singularities and enhanced gauge symmetries, Nucl. Phys. B 481 (1996) 215 [hep-th/9605200] [INSPIRE].
S. Katz, D.R. Morrison, S. Schäfer-Nameki and J. Sully, Tate’s algorithm and F-theory, JHEP 08 (2011) 094 [arXiv:1106.3854] [INSPIRE].
C. Lawrie and S. Schäfer-Nameki, The Tate form on steroids: resolution and higher codimension fibers, JHEP 04 (2013) 061 [arXiv:1212.2949] [INSPIRE].
H. Hayashi, C. Lawrie, D.R. Morrison and S. Schäfer-Nameki, Box graphs and singular fibers, JHEP 05 (2014) 048 [arXiv:1402.2653] [INSPIRE].
J. Marsano, N. Saulina and S. Schäfer-Nameki, Monodromies, fluxes, and compact three-generation F-theory GUTs, JHEP 08 (2009) 046 [arXiv:0906.4672] [INSPIRE].
J. Marsano and S. Schäfer-Nameki, Yukawas, G-flux, and spectral covers from resolved Calabi-Yau’s, JHEP 11 (2011) 098 [arXiv:1108.1794] [INSPIRE].
S. Krause, C. Mayrhofer and T. Weigand, G4 flux, chiral matter and singularity resolution in F-theory compactifications, Nucl. Phys. B 858 (2012) 1 [arXiv:1109.3454] [INSPIRE].
M. Esole, P. Jefferson and M.J. Kang, Euler characteristics of Crepant resolutions of Weierstrass models, Commun. Math. Phys. 371 (2019) 99 [arXiv:1703.00905] [INSPIRE].
U. Derenthal, Singular del Pezzo surfaces whose universal torsors are hypersurfaces, math/0604194.
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Hübner, M. 5d SCFTs from (En, Em) conformal matter. J. High Energ. Phys. 2020, 14 (2020). https://doi.org/10.1007/JHEP12(2020)014
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DOI: https://doi.org/10.1007/JHEP12(2020)014