Abstract
Extending results of 1112.3984, we show that all rank 1 \( \mathcal{N}=2 \) SCFT’s in the sequence H 1, H 2, D 4 E 6, E 7, E 8 have canonical finite BPS chambers containing precisely 2h(F) = 12(∆ − 1) hypermultiplets. The BPS spectrum of the canonical BPS chambers saturates the conformal central charge c, and satisfies some intriguing numerology.
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C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F -theory on Calabi-Yau threefolds. 1, Nucl. Phys. B 473 (1996) 74 [hep-th/9602114] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2., Nucl. Phys. B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
T. Banks, M.R. Douglas and N. Seiberg, Probing F -theory with branes, Phys. Lett. B 387 (1996) 278 [hep-th/9605199] [INSPIRE].
K. Dasgupta and S. Mukhi, F -theory at constant coupling, Phys. Lett. B 385 (1996) 125 [hep-th/9606044] [INSPIRE].
J.A. Minahan and D. Nemeschansky, An N = 2 superconformal fixed point with E 6 global symmetry, Nucl. Phys. B 482 (1996) 142 [hep-th/9608047] [INSPIRE].
J. Minahan and D. Nemeschansky, Superconformal Fixed Points with E n Global Symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076].
O. Aharony and Y. Tachikawa, A holographic computation of the central charges of D = 4, N = 2 SCFTs, JHEP 01 (2008) 037 [arXiv:0711.4532] [INSPIRE].
S. Cecotti, A. Neitzke and C. Vafa, R-Twisting and 4d/2d Correspondences, arXiv:1006.3435 [INSPIRE].
M. Alim et al., N = 2 Quantum Field Theories and Their BPS Quivers, arXiv:1112.3984 [INSPIRE].
S. Cecotti, M. Del Zotto and S. Giacomelli, More on the N = 2 superconformal systems of type D p (G), arXiv:1303.3149 [INSPIRE].
S. Cecotti and M. Del Zotto, Infinitely many N = 2 SCFT with ADE flavor symmetry, JHEP 01 (2013) 191 [arXiv:1210.2886] [INSPIRE].
P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].
D. Xie and P. Zhao, Central charges and RG flow of strongly-coupled \( \mathcal{N}=2 \) theory, JHEP 03 (2013) 006 [arXiv:1301.0210] [INSPIRE].
S. Cecotti and M. Del Zotto, On Arnold’s 14 ‘exceptional’ \( \mathcal{N}=2 \) superconformal gauge theories, JHEP 10 (2011) 099 [arXiv:1107.5747] [INSPIRE].
S. Cecotti, The quiver approach to the BPS spectrum of a 4d N = 2 gauge theory, arXiv:1212.3431 [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Framed BPS States, arXiv:1006.0146 [INSPIRE].
S. Cecotti and C. Vafa, Classification of complete \( \mathcal{N}=2 \) supersymmetric theories in 4 dimensions, to appear in Surveys in differential geometry. Vol. 18, International Press, Boston U.S.A. (2013) arXiv:1103.5832 [INSPIRE].
S. Cecotti, Categorical tinkertoys for \( \mathcal{N}=2 \) gauge theories, Int. J. Mod. Phys. A 28 (2013) 1330006 [arXiv:1203.6734] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
D. Berenstein and M.R. Douglas, Seiberg duality for quiver gauge theories, hep-th/0207027 [INSPIRE].
H. Derksen, J. Wyman and A. Zelevinsky, Quivers with potentials and their representations I: Mutations, Selecta Math. 14 (2008) 59.
B. Keller, Quiver mutation in Java, available from the author’s homepage, http://www.institut.math.jussieu.fr/~keller/quivermutation.
S. Fomin and A. Zelevinsky, Cluster algebras IV: Coefficients, Compos. Math. 143 (2007) 112.
T. Nakanishi and A. Zelevinsky, On tropical dualities in cluster algebras, arXiv:1101.3736.
B. Keller, Cluster algebras and derived categories, arXiv:1202.4161.
M. Kontsevich and Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, arXiv:0811.2435 [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Four-dimensional wall-crossing via three-dimensional field theory, Commun. Math. Phys. 299 (2010) 163 [arXiv:0807.4723] [INSPIRE].
T. Dimofte and S. Gukov, Refined, Motivic and Quantum, Lett. Math. Phys. 91 (2010) 1 [arXiv:0904.1420] [INSPIRE].
S. Cecotti and C. Vafa, BPS Wall Crossing and Topological Strings, arXiv:0910.2615 [INSPIRE].
T. Dimofte, S. Gukov and Y. Soibelman, Quantum Wall Crossing in N = 2 Gauge Theories, Lett. Math. Phys. 95 (2011) 1 [arXiv:0912.1346] [INSPIRE].
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ArXiv ePrint: 1304.0614
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Cecotti, S., Del Zotto, M. The BPS spectrum of the 4d \( \mathcal{N}=2 \) SCFT’s H 1, H 2, D 4, E 6, E 7, E 8 . J. High Energ. Phys. 2013, 75 (2013). https://doi.org/10.1007/JHEP06(2013)075
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DOI: https://doi.org/10.1007/JHEP06(2013)075