Abstract
According to a conjecture, all 5d SCFTs should be obtainable by rank- preserving RG flows of 6d SCFTs compactified on a circle possibly twisted by a background for the discrete global symmetries around the circle. For a 6d SCFT admitting an F-theory construction, its untwisted compactification admits a dual M-theory description in terms of a “parent” Calabi-Yau threefold which captures the Coulomb branch of the compacti- fied 6d SCFT. The RG flows to 5d SCFTs can then be identified with a sequence of flop transitions and blowdowns of the parent Calabi-Yau leading to “descendant” Calabi-Yau threefolds which describe the Coulomb branches of the resulting 5d SCFTs. An explicit description of parent Calabi-Yaus is known for untwisted compactifications of rank one 6d SCFTs. In this paper, we provide a description of parent Calabi-Yaus for untwisted compactifications of arbitrary rank 6d SCFTs. Since 6d SCFTs of arbitrary rank can be viewed as being constructed out of rank one SCFTs, we accomplish the extension to arbi- trary rank by identifying a prescription for gluing together Calabi-Yaus associated to rank one 6d SCFTs.
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References
P. Jefferson, S. Katz, H.-C. Kim and C. Vafa, On geometric classification of 5d SCFTs, JHEP 04 (2018) 103 [arXiv:1801.04036] [INSPIRE].
P. Jefferson, H.-C. Kim, C. Vafa and G. Zafrir, Towards classification of 5d SCFTs: single gauge node, arXiv:1705.05836 [INSPIRE].
L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: rank one, JHEP 07 (2019) 178 [arXiv:1809.01650] [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].
L. Bhardwaj, D.R. Morrison, Y. Tachikawa and A. Tomasiello, The frozen phase of F-theory, JHEP 08 (2018) 138 [arXiv:1805.09070] [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].
L. Bhardwaj, Classification of 6d N = (1, 0) gauge theories, JHEP 11 (2015) 002 [arXiv:1502.06594] [INSPIRE].
A. Hanany and A. Zaffaroni, Branes and six-dimensional supersymmetric theories, Nucl. Phys. B 529 (1998) 180 [hep-th/9712145] [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].
M. Esole and S.-H. Shao, M-theory on elliptic Calabi-Yau threefolds and 6d anomalies, arXiv:1504.01387 [INSPIRE].
M. Esole, R. Jagadeesan and M.J. Kang, The geometry of G2 , Spin(7) and Spin(8)-models, arXiv:1709.04913 [INSPIRE].
M. Esole, P. Jefferson and M.J. Kang, The geometry of F 4 -models, arXiv:1704.08251 [INSPIRE].
M. Esole, S.-H. Shao and S.-T. Yau, Singularities and gauge theory phases II, Adv. Theor. Math. Phys. 20 (2016) 683 [arXiv:1407.1867] [INSPIRE].
M. Esole, S.-H. Shao and S.-T. Yau, Singularities and gauge theory phases, Adv. Theor. Math. Phys. 19 (2015) 1183 [arXiv:1402.6331] [INSPIRE].
M. Esole and S.-T. Yau, Small resolutions of SU(5)-models in F-theory, Adv. Theor. Math. Phys. 17 (2013) 1195 [arXiv:1107.0733] [INSPIRE].
M. Esole and M.J. Kang, The geometry of the SU(2) × G 2 -model, JHEP 02 (2019) 091 [arXiv:1805.03214] [INSPIRE].
M. Esole and M.J. Kang, Flopping and slicing: SO(4) and Spin(4)-models, arXiv:1802.04802 [INSPIRE].
M. Esole, M.J. Kang and S.-T. Yau, Mordell-Weil torsion, anomalies and phase transitions, arXiv:1712.02337 [INSPIRE].
N. Seiberg, Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B 388 (1996) 753 [hep-th/9608111] [INSPIRE].
A. Grassi and D.R. Morrison, Anomalies and the Euler characteristic of elliptic Calabi-Yau threefolds, Commun. Num. Theor. Phys. 6 (2012) 51 [arXiv:1109.0042] [INSPIRE].
D.R. Morrison and W. Taylor, Classifying bases for 6D F-theory models, Central Eur. J. Phys. 10 (2012) 1072 [arXiv:1201.1943] [INSPIRE].
M. Taki, Seiberg duality, 5d SCFTs and Nekrasov partition functions, arXiv:1401.7200 [INSPIRE].
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. Sch¨afer-Nameki and J. Sully, Tate’s algorithm and F-theory, JHEP 08 (2011) 094 [arXiv:1106.3854] [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].
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. D 93 (2016) 086002 [Erratum ibid. D 100 (2019) 029901] [arXiv:1511.05565] [INSPIRE].
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Bhardwaj, L., Jefferson, P. Classifying 5d SCFTs via 6d SCFTs: arbitrary rank. J. High Energ. Phys. 2019, 282 (2019). https://doi.org/10.1007/JHEP10(2019)282
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DOI: https://doi.org/10.1007/JHEP10(2019)282