Abstract
We consider field theory side of new multiple Seiberg dualities conjectured within superconformal index matching approach. We study the case of SU(2) supersymmetric QCD and find that the numerous conjectured duals are different faces of handful of master theories. These different faces are inequivalent to each other in a very peculiar sense. Some master theories are fully known; we construct superpotentials for others. We confirm that all index identities correspond to theories flowing to one and the same theory in the infrared, thus supporting the conjecture of index matching for Seiberg dual theories. However, none of the index identities considered in this paper actually implies an entirely new, unknown duality.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Romelsberger, Calculating the superconformal index and Seiberg duality, arXiv:0707.3702 [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].
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, 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 and G.S. Vartanov, Superconformal indices for N = 1 theories with multiple duals, Nucl. Phys. B 824 (2010) 192 [arXiv:0811.1909] [SPIRES].
V.P. Spiridonov, Theta hypergeometric integrals, Algebra i Analiz 15 (6) (2003) 161 [St. Petersburg Math. J. 15 (2003) 929] [math/0303205].
V.P. Spiridonov, Essays on the theory of elliptic hypergeometric functions, Uspekhi Mat. Nauk 63 (2008) 3 [Russian Math. Surveys 63 (2008) 405] [arXiv:0805.3135].
E.M. Rains, Transformations of elliptic hypergometric integrals, to be published in Ann. of Math., math/0309252.
E.M. Rains, BC n -symmetric abelian functions, Duke Math. J. 135 (2006) 99 [math/0402113].
V.P. Spiridonov and G.S. Vartanov, Elliptic hypergeometry of supersymmetric dualities, arXiv:0910.5944 [SPIRES].
N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D 49 (1994) 6857 [hep-th/9402044] [SPIRES].
R.G. Leigh and M.J. Strassler, Accidental symmetries and N = 1 duality in supersymmetric gauge theory, Nucl. Phys. B 496 (1997) 132 [hep-th/9611020] [SPIRES].
N. Seiberg, Electric-magnetic duality in supersymmetric non-abelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [SPIRES].
C. Csáki, M. Schmaltz, W. Skiba and J. Terning, Self-dual N = 1 SUSY gauge theories, Phys. Rev. D 56 (1997) 1228 [hep-th/9701191] [SPIRES].
K.A. Intriligator and P. Pouliot, Exact superpotentials, quantum vacua and duality in supersymmetric SP(N(c)) gauge theories, Phys. Lett. B 353 (1995) 471 [hep-th/9505006] [SPIRES].
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Adv. Study Inst. Ser. B Phys. 59 (1980) 135 [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 0912.4523
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Khmelnitsky, A. Interpreting multiple dualities conjectured from superconformal index identities. J. High Energ. Phys. 2010, 65 (2010). https://doi.org/10.1007/JHEP03(2010)065
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2010)065