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N=2 Dualities and Z Extremization in Three Dimensions · Around

2011

N=2 Dualities and Z Extremization in Three Dimensions

Willett, Brian, Yaakov, Itamar

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We use localization techniques to study duality in N = 2 supersymmetric gauge theories in three dimensions.

Specifically, we consider a duality due to Aharony involving unitary and symplectic gauge groups, which is similar to Seiberg duality in four dimensions, as well as related dualities involving Chern-Simons terms.
These theories have the possibility of non-trivial anomalous dimensions for the chiral multiplets and were previously difficult to examine.
We use a matrix model to compute the partition functions on both sides of the duality, deformed by real mass and FI terms, and find that they agree.

Built on

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O. Aharony, A. Hanany, K. A. Intriligator et al
1997
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O. Aharony, “IR duality in d = 3 N=2 supersymmetric USp(2N(c)) and U(N(c)) gauge theories,” Phys. Lett. B404
1997
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Similar

J. de Boer, K. Hori, H. Ooguri et al
1997
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J. de Boer, K. Hori, H. Ooguri et al
1997
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A. Hanany and E. Witten, “Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics,” Nucl. Phys. B 492
1997
Cited alongside, same era.
V. Borokhov, A. Kapustin and X. k. Wu, “Monopole operators and mirror symmetry in three dimensions,” JHEP 0212
2002
Cited alongside, same era.
V. Pestun, “Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops,” arXiv:0906.0638 [hep-th]
Original
Cited in the paper.
A. Kapustin, B. Willett and I. Yaakov, “Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter,” arXiv:0909.4559 [hep-th]
Original
Cited in the paper.
A. Kapustin, B. Willett and I. Yaakov, “Nonperturbative Tests of Three-Dimensional Dualities,” arXiv:1003.5694 [hep-th]
Original
Cited in the paper.
D. L. Jafferis, “The Exact Superconformal R-Symmetry Extremizes Z,” arXiv:1012.3210 [hep-th]
Original
Cited in the paper.
A. Kapustin, B. Willett and I. Yaakov, “Tests of Seiberg-like Duality in Three Dimensions,” arXiv:1012.4021 [hep-th]
Original
Cited in the paper.
N. Hama, K. Hosomichi and S. Lee, “SUSY Gauge Theories on Squashed Three-Spheres,” arXiv:1102.4716 [hep-th]
Original
Cited in the paper.
N. Hama, K. Hosomichi and S. Lee, “Notes on SUSY Gauge Theories on Three-Sphere,” arXiv:1012.3512 [hep-th]
Original
Cited in the paper.

Then

O. Aharony, O. Bergman, D. L. Jafferis, “Fractional M2-branes,” JHEP 0811
Original
2008
Later among the works it cites.
F. van de Bult “Hyperbolic Hypergeometric Functions,” Thesis (2008)
2008
Later among the works it cites.
A. Giveon and D. Kutasov, “Seiberg Duality in Chern-Simons Theory,” Nucl. Phys. B 812
Original
2009
Later among the works it cites.
E. Rains “Transformations of elliptic hypergeometric integrals,” Annals of Mathematics, 171 (2010), 169243
2010
Later among the works it cites.

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