Abstract
We derive an integral representation for the superconformal index of the strongly-coupled \( \mathcal{N} = 2 \) superconformal field theory with E 6 flavor symmetry. The explicit expression of the index allows highly non-trivial checks of Argyres-Seiberg duality and of a class of S-dualities conjectured by Gaiotto.
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D. Gaiotto, N = 2 dualities, arXiv:0904.2715 [SPIRES].
N.A. Nekrasov, Seiberg-Witten Prepotential From Instanton Counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [SPIRES].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [SPIRES].
N. Wyllard, A N−1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189] [SPIRES].
A. Gadde, E. Pomoni, L. Rastelli and S.S. Razamat, S-duality and 2d Topological QFT, JHEP 03 (2010) 032 [arXiv:0910.2225] [SPIRES].
J. Kinney, J.M. Maldacena, S. Minwalla and S. Raju, An index for 4 dimensional super conformal theories, Commun. Math. Phys. 275 (2007) 209 [hep-th/0510251] [SPIRES].
F.J. van de Bult, An elliptic hypergeometric integral with w(f 4) symmetry, arXiv:0909.4793.
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [SPIRES].
P.C. Argyres and J.R. Wittig, Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories, JHEP 01 (2008) 074 [arXiv:0712.2028] [SPIRES].
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] [SPIRES].
V.P. Spiridonov and S.O. Warnaar, Inversions of integral operators and elliptic beta integrals on root systems, Adv. Math. 207 (2006) 91 [math/0411044].
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] [SPIRES].
D. Gaiotto, A. Neitzke and Y. Tachikawa, Argyres-Seiberg duality and the Higgs branch, Commun. Math. Phys. 294 (2010) 389 [arXiv:0810.4541] [SPIRES].
C. Romelsberger, Counting chiral primaries in N = 1, D = 4 superconformal field theories, Nucl. Phys. B 747 (2006) 329 [hep-th/0510060] [SPIRES].
F.A. Dolan and H. Osborn, On short and semi-short representations for four dimensional superconformal symmetry, Ann. Phys. 307 (2003) 41 [hep-th/0209056] [SPIRES].
F.A. Dolan and H. Osborn, Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N = 1 Dual Theories, Nucl. Phys. B 818 (2009) 137 [arXiv:0801.4947] [SPIRES].
V.P. Spiridonov, On the elliptic beta function, Uspekhi Mat. Nauk 56 (2001) 181.
J . van Diejen and V. Spiridonov, Elliptic Beta Integrals and Mudular Hypergeometric Sums: An Overview, Rocky Mountain J. Math. 32 (2002) 639.
V. Spiridonov, Essays on the theory of elliptic hypergeometric functions, Uspekhi Mat. Nauk 63 (2008) 3 [arXiv:0805.3135].
V. Spiridonov, Classical elliptic hypergeometric functions and their applications, Rokko Lect. in Math. 18 (2005) 253 [math/0511579].
E. M. Rains, Transformations of Elliptic Hypergeometric Integrals, math/0309252.
C. Romelsberger, Calculating the Superconformal Index and Seiberg Duality, arXiv:0707.3702 [SPIRES].
V.P. Spiridonov and G.S. Vartanov, Superconformal indices for \( \mathcal{N} = 1 \) theories with multiple duals, Nucl. Phys. B 824 (2010) 192 [arXiv:0811.1909] [SPIRES].
V.P. Spiridonov and G.S. Vartanov, Elliptic hypergeometry of supersymmetric dualities, arXiv:0910.5944 [SPIRES].
A. Gadde, E. Pomoni and L. Rastelli, The Veneziano Limit of N = 2 Superconformal QCD: Towards the String Dual of N = 2 SU(N c ) SYM with N f = 2N c , arXiv:0912.4918 [SPIRES].
M.R. Gaberdiel and B. Zwiebach, Exceptional groups from open strings, Nucl. Phys. B 518 (1998) 151 [hep-th/9709013] [SPIRES].
J.A. Minahan and D. Nemeschansky, Superconformal fixed points with E (n) global symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076] [SPIRES].
F. Benini, S. Benvenuti and Y. Tachikawa, Webs of five-branes and N = 2 superconformal field theories, JHEP 09 (2009) 052 [arXiv:0906.0359] [SPIRES].
R. Slansky, Group Theory for Unified Model Building, Phys. Rept. 79 (1981) 1 [SPIRES].
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ArXiv ePrint: 1003.4244
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Gadde, A., Rastelli, L., Razamat, S.S. et al. The superconformal index of the E 6 SCFT. J. High Energ. Phys. 2010, 107 (2010). https://doi.org/10.1007/JHEP08(2010)107
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DOI: https://doi.org/10.1007/JHEP08(2010)107