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2011

N=2 supersymmetric theories on squashed three-sphere

Imamura, Yosuke, Yokoyama, Daisuke

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We investigate a squashing deformation of 3d N=2 supersymmetric theories on three-sphere, which have four supercharges.

The deformation preserves SU(2)_L x U(1)_r isometry and all four supersymmetries.
We compute the partition function and find non-trivial dependence on the squashing parameter.
We also consider the large N limit of a certain class of quiver gauge theories which have free energy of order N^{3/2}, and show that the free energy on the squashed sphere differs from that on round sphere by a certain factor depending only on the squashing parameter.

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A. Kapustin, B. Willett, I. Yaakov, “Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter,” JHEP 1003
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Similar

Y. Imamura and S. Yokoyama, “Index for three dimensional superconformal field theories with general R-charge assignments,” JHEP 1104
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N. Hama, K. Hosomichi and S. Lee, “Notes on SUSY Gauge Theories on Three-Sphere,” JHEP 1103
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N. Drukker, M. Marino, P. Putrov, “From weak to strong coupling in ABJM theory,” Commun. Math. Phys. 306
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C. P. Herzog, I. R. Klebanov, S. S. Pufu and T. Tesileanu, “Multi-Matrix Models and Tri-Sasaki Einstein Spaces,” Phys. Rev. D 83
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D. L. Jafferis, I. R. Klebanov, S. S. Pufu, B. R. Safdi, “Towards the F-Theorem: N=2 Field Theories on the Three-Sphere,” JHEP 1106

Then

Y. Imamura, D. Yokoyama and S. Yokoyama, “Superconformal index for large N quiver Chern-Simons theories,” JHEP 1108
Original
2011
Closest in time.
C. Hwang, H. Kim, K. -J. Park, J. Park, “Index computation for 3d Chern-Simons matter theory: test of Seiberg-like duality,” JHEP 1109
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N. Hama, K. Hosomichi and S. Lee, “SUSY Gauge Theories on Squashed Three-Spheres,” JHEP 1105
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Y. Imamura, “Relation between the 4d superconformal index and the S 3 partition function,” JHEP 1109
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Original

2011

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D. L. Jafferis, “The Exact Superconformal R-Symmetry Extremizes Z,” arXiv:1012.3210 [hep-th]

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A. Kapustin, B. Willett, I. Yaakov, “Tests of Seiberg-like Duality in Three Dimensions,” [arXiv:1012.4021 [hep-th]]

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A. Kapustin, “Seiberg-like duality in three dimensions for orthogonal gauge groups,” arXiv:1104.0466 [hep-th]

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B. Willett and I. Yaakov, “N=2 Dualities and Z Extremization in Three Dimensions,” arXiv:1104.0487 [hep-th]

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F. A. H. Dolan, V. P. Spiridonov, G. S. Vartanov, “From 4d superconformal indices to 3d partition functions,” [arXiv:1104.1787 [hep-th]]

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D. Jafferis, X. Yin, “A Duality Appetizer,” [arXiv:1103.5700 [hep-th]]

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F. Benini, C. Closset, S. Cremonesi, “Comments on 3d Seiberg-like dualities,” [arXiv:1108.5373 [hep-th]]

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