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## Superconformal indices of three-dimensional theories related by mirror symmetry,” arXiv:1103.4075 [hep-th

Citations: | 38 - 3 self |

### Citations

684 |
N=6 superconformal ChernSimons-matter theories, M2-branes and their gravity duals,” arXiv:0806.1218 [hep-th
- Aharony, Bergman, et al.
(Show Context)
Citation Context ...ensional supersymmetric Chern–Simons theories with large rank of the gauge group N was introduced, and the coincidence with the gravitational background index in the context of AdS/CFT correspondence =-=[11]-=- has been established. In [12] superconformal characters of three-dimensional supersymmetric theories have been constructed and, after taking restrictions for parameters in them, SCIs for theories con... |

202 |
An index for 4 dimensional super conformal theories
- Kinney, Maldacena, et al.
(Show Context)
Citation Context ...uction The superconformal index (SCI) technique is a very useful tool for testing supersymmetric dualities. Initially, this technique was introduced for four-dimensional supersymmetric field theories =-=[1, 2]-=- in the context of N = 1 SYM Seiberg dualities and AdS/CFT correspondence for N = 4 SYM field theories. In this case, the indices are described by the elliptic hypergeometric integrals [3] as observed... |

200 | The Exact Superconformal R-Symmetry Extremizes Z,” [arXiv:1012.3210
- Jafferis
(Show Context)
Citation Context ... various three-dimensional SCIs were calculated in the large N limit for comparison with their gravity duals. The partition functions of three-dimensional supersymmetric field theories are studied in =-=[18, 19, 20, 21, 22, 23, 24, 25]-=-. The superconformal index for N = 6 Chern–Simons theory with finite N was derived by Kim in [14]. The contribution to SCIs of chiral fields with arbitrary R-charge was found recently by Imamura and Y... |

165 | Mirror symmetry in three-dimensional gauge theories
- Intriligator, Seiberg
- 1996
(Show Context)
Citation Context ... consequences of the mirror symmetry for three-dimensionalN = 2 supersymmetric field theory with U(1) gauge group and Nf = 1 in its IR fixed point, whose mirror partner is the free Wess–Zumino theory =-=[27, 28, 29]-=-. The initial electric theory has one flavour or two quark superfields Q and Q̃ of charges +1 and −1 and R-charges ∆Q = ∆Q̃ = 1/3. The superconformal index is given by the expression Ie,Nf=1 = ∑ k∈Z q... |

150 |
From weak to strong coupling
- Drukker, Marino, et al.
(Show Context)
Citation Context ... various three-dimensional SCIs were calculated in the large N limit for comparison with their gravity duals. The partition functions of three-dimensional supersymmetric field theories are studied in =-=[18, 19, 20, 21, 22, 23, 24, 25]-=-. The superconformal index for N = 6 Chern–Simons theory with finite N was derived by Kim in [14]. The contribution to SCIs of chiral fields with arbitrary R-charge was found recently by Imamura and Y... |

73 | Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories, Nucl. Phys. B818
- Dolan, Osborn
- 2009
(Show Context)
Citation Context ...M Seiberg dualities and AdS/CFT correspondence for N = 4 SYM field theories. In this case, the indices are described by the elliptic hypergeometric integrals [3] as observed first by Dolan and Osborn =-=[4]-=-. Various developments and applications of this technique are described in [5, 6, 7, 8, 9]. Later, in [10], the superconformal index for three-dimensional supersymmetric Chern–Simons theories with lar... |

72 | Index for three dimensional superconformal field theories with general R-charge assignments
- Imamura, Yokoyama
- 2011
(Show Context)
Citation Context ...conformal index for N = 6 Chern–Simons theory with finite N was derived by Kim in [14]. The contribution to SCIs of chiral fields with arbitrary R-charge was found recently by Imamura and Yokoyama in =-=[26]-=-. After combining everything, this gives an exact formula for 3d SCIs analogous to Römelsberger’s result for 4d N = 1 SYM theories [2]. SCIs of some 3d N = 2 supersymmetric field theories and their m... |

57 | Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
- Spiridonov, Vartanov
(Show Context)
Citation Context ...n this case, the indices are described by the elliptic hypergeometric integrals [3] as observed first by Dolan and Osborn [4]. Various developments and applications of this technique are described in =-=[5, 6, 7, 8, 9]-=-. Later, in [10], the superconformal index for three-dimensional supersymmetric Chern–Simons theories with large rank of the gauge group N was introduced, and the coincidence with the gravitational ba... |

51 |
supersymmetric gauge theories in three dimensions,”
- Aharony, Hanany, et al.
- 1997
(Show Context)
Citation Context ...this gives an exact formula for 3d SCIs analogous to Römelsberger’s result for 4d N = 1 SYM theories [2]. SCIs of some 3d N = 2 supersymmetric field theories and their mirror partners [27] (see also =-=[28, 29]-=- for a general discussion of such theories) were computed in [26] and their coincidence was confirmed up to the first several terms of the corresponding series expansions in chemical potentials. The m... |

50 |
Calculating the partition function
- Cheon, Kim, et al.
(Show Context)
Citation Context ... various three-dimensional SCIs were calculated in the large N limit for comparison with their gravity duals. The partition functions of three-dimensional supersymmetric field theories are studied in =-=[18, 19, 20, 21, 22, 23, 24, 25]-=-. The superconformal index for N = 6 Chern–Simons theory with finite N was derived by Kim in [14]. The contribution to SCIs of chiral fields with arbitrary R-charge was found recently by Imamura and Y... |

46 | Multi-Matrix Models and Tri-Sasaki Einstein Spaces,” arXiv:1011.5487 [hep-th
- Herzog, Klebanov, et al.
(Show Context)
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44 |
The large N limit of quiver matrix models and Sasaki-Einstein manifolds, arXiv:1102.5289. * Temporary entry
- Martelli, Sparks
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39 | Basic Hypergeometric Series, 2nd Edition - Gasper, Rahman - 2004 |

34 | Superconformal indices for N = 1 theories with multiple duals, Nucl. Phys. B824
- Spiridonov, Vartanov
- 2010
(Show Context)
Citation Context ...n this case, the indices are described by the elliptic hypergeometric integrals [3] as observed first by Dolan and Osborn [4]. Various developments and applications of this technique are described in =-=[5, 6, 7, 8, 9]-=-. Later, in [10], the superconformal index for three-dimensional supersymmetric Chern–Simons theories with large rank of the gauge group N was introduced, and the coincidence with the gravitational ba... |

29 | Exact results for Wilson loops in superconformal Chern–Simons theories with matter
- Kapustin, Willett, et al.
- 2010
(Show Context)
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23 |
On the elliptic beta function
- Spiridonov
(Show Context)
Citation Context ...theories [1, 2] in the context of N = 1 SYM Seiberg dualities and AdS/CFT correspondence for N = 4 SYM field theories. In this case, the indices are described by the elliptic hypergeometric integrals =-=[3]-=- as observed first by Dolan and Osborn [4]. Various developments and applications of this technique are described in [5, 6, 7, 8, 9]. Later, in [10], the superconformal index for three-dimensional sup... |

21 |
Elliptic beta integrals and solvable models of statistical mechanics
- Spiridonov
(Show Context)
Citation Context ...n this case, the indices are described by the elliptic hypergeometric integrals [3] as observed first by Dolan and Osborn [4]. Various developments and applications of this technique are described in =-=[5, 6, 7, 8, 9]-=-. Later, in [10], the superconformal index for three-dimensional supersymmetric Chern–Simons theories with large rank of the gauge group N was introduced, and the coincidence with the gravitational ba... |

21 |
On Superconformal Characters and Partition Functions in Three Dimensions,
- Dolan
- 2010
(Show Context)
Citation Context ...Simons theories with large rank of the gauge group N was introduced, and the coincidence with the gravitational background index in the context of AdS/CFT correspondence [11] has been established. In =-=[12]-=- superconformal characters of three-dimensional supersymmetric theories have been constructed and, after taking restrictions for parameters in them, SCIs for theories considered in [10] can be obtaine... |

17 |
An index to count chiral primaries in N = 1 d = 4 superconformal field theories,” arXiv:hep-th/0510060. 59
- Romelsberger
(Show Context)
Citation Context ...uction The superconformal index (SCI) technique is a very useful tool for testing supersymmetric dualities. Initially, this technique was introduced for four-dimensional supersymmetric field theories =-=[1, 2]-=- in the context of N = 1 SYM Seiberg dualities and AdS/CFT correspondence for N = 4 SYM field theories. In this case, the indices are described by the elliptic hypergeometric integrals [3] as observed... |

14 |
Branes and mirror symmetry in N = 2 supersymmetric gauge theories in three dimensions
- Boer, Hori, et al.
- 1997
(Show Context)
Citation Context ...this gives an exact formula for 3d SCIs analogous to Römelsberger’s result for 4d N = 1 SYM theories [2]. SCIs of some 3d N = 2 supersymmetric field theories and their mirror partners [27] (see also =-=[28, 29]-=- for a general discussion of such theories) were computed in [26] and their coincidence was confirmed up to the first several terms of the corresponding series expansions in chemical potentials. The m... |

13 |
The Complete superconformal index for N
- Kim
(Show Context)
Citation Context ...s of three-dimensional supersymmetric theories have been constructed and, after taking restrictions for parameters in them, SCIs for theories considered in [10] can be obtained in a different way. In =-=[13, 14, 15, 16, 17]-=-, various three-dimensional SCIs were calculated in the large N limit for comparison with their gravity duals. The partition functions of three-dimensional supersymmetric field theories are studied in... |

8 | Superconformal indices for orbifold Chern–Simons theories
- Choi, Lee, et al.
(Show Context)
Citation Context ...s of three-dimensional supersymmetric theories have been constructed and, after taking restrictions for parameters in them, SCIs for theories considered in [10] can be obtained in a different way. In =-=[13, 14, 15, 16, 17]-=-, various three-dimensional SCIs were calculated in the large N limit for comparison with their gravity duals. The partition functions of three-dimensional supersymmetric field theories are studied in... |

7 | On the ISS model of dynamical - Vartanov |

7 |
Superconformal index for large N quiver Chern–Simons theories, arXiv:1102.0621 [hep-th
- Imamura, Yokoyama, et al.
(Show Context)
Citation Context ...s of three-dimensional supersymmetric theories have been constructed and, after taking restrictions for parameters in them, SCIs for theories considered in [10] can be obtained in a different way. In =-=[13, 14, 15, 16, 17]-=-, various three-dimensional SCIs were calculated in the large N limit for comparison with their gravity duals. The partition functions of three-dimensional supersymmetric field theories are studied in... |

7 |
Notes on SUSY Gauge Theories on Three-Sphere
- Hama, Hosomichi, et al.
(Show Context)
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6 | Probing AdS4/CFT3 proposals beyond chiral rings - Kim, Park |

4 |
Refined test of AdS4/CFT3 correspondence for
- Cheon, Gang, et al.
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3 |
Indices for superconformal field theories in 3, 5 and 6 dimensions”, Journal of High Energy Physics 2008, 064. • “The complete superconformal index for Chern-Simons theory”, Nuclear Physics B 821, 241 (2009). • “Index for three dimensional superconformal
- Bhattacharya, Bhattacharyya, et al.
- 2011
(Show Context)
Citation Context ...e described by the elliptic hypergeometric integrals [3] as observed first by Dolan and Osborn [4]. Various developments and applications of this technique are described in [5, 6, 7, 8, 9]. Later, in =-=[10]-=-, the superconformal index for three-dimensional supersymmetric Chern–Simons theories with large rank of the gauge group N was introduced, and the coincidence with the gravitational background index i... |

3 |
On group theoretical aspects, hypergeometric transformations and symmetries of angular momentum coefficients
- Krattenthaler, Rao
- 2004
(Show Context)
Citation Context ...y group of the 2φ1-series is generated by repeated applications of this transformation together with the permutation of its numerator parameters A and B, and it is isomorphic to the dihedral group D6 =-=[31]-=-. This leads to two further 2φ1-transformation formulas, namely (see [30, (1.4.5)]) 2φ1 [ A,B C ; q, Z ] = (C/B,BZ; q)∞ (C,Z; q)∞ 2φ1 [ ABZ/C,B BZ ; q, C B ] (37) and (see [30, (1.4.6)]) 2φ1 [ A,B C ;... |

2 |
Quantum dynamics of the D = 3 abelian Higgs model and spontaneous breaking of parity, Phys
- Spiridonov
- 1990
(Show Context)
Citation Context ...ion of total ellipticity, which is interpreted from the physical point of view as the ’t Hooft anomaly matching conditions [6]. The only somewhat analogous notion is the parity anomaly [29] (see also =-=[32]-=- for early references and a perturbative analysis of this phenomenon), which is associated with the classical Chern–Simons term breaking the parity. As to reduction of the number of flavours, in the 4... |

2 |
New and old N = 8 superconformal field theories in three dimensions, arXiv:1103.3548 [hep-th
- Bashkirov, Kapustin
(Show Context)
Citation Context ... his visit in February 2011, for its warm hospitality. Additionally, V.S. and G.V. thank the Heisenberg–Landau program for financial support. Note added. After finishing this work, we became aware of =-=[33]-=-, where SCIs induced by the topological charge of the group U(1)J are considered for 3d N = 8 theories, which partially overlaps with our considerations. Furthermore, the revised version of [16], whic... |

1 |
S-Duality and 2d topological QFT, J. High Energy Phys
- Gadde, Pomoni, et al.
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