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Rings of short N=3 superfields in three dimensions and M-theory on AdS_4 x N^{0,1,0}
High Energy Physics - Theory · Submitted 24 May 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This and other arguments identify the N=3 superconformal field theory dual to M-theory compactified on AdS_4 x N^{0,1,0}.
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In this paper we investigate three-dimensional superconformal gauge theories with N=3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N=3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N=2 theories. When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart of the ring defined by the algebraic geometry of the 8-dimensional cone transverse to the brane. This and other arguments identify the N=3 superconformal field theory dual to M-theory compactified on AdS_4 x N^{0,1,0}. It is an N=3 gauge theory with SU(N) x SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern Simons interaction. The AdS/CFT correspondence can be directly verified using the recently worked out Kaluza Klein spectrum of N^{0,1,0} and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin 3/2 N=3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N=4 theory. We investigate this intriguing and inspiring feature in a separate paper.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we investigate three-dimensional superconformal gauge theories with N=3 supersymmetry. | contribution 0.67 | 0.89 | 0.03 | asserted 0.87 |
| s1 | Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N=3 superfields. | contribution 0.71 | 0.96 | 0.06 | asserted 1.00 |
| s2 | We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N=2 theories. | result 0.97 | 0.95 | 0.11 | asserted 1.00 |
| s3 | When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart of the ring defined by the algebraic geometry of the 8-dimensional cone transverse to the brane. | interpretation 0.72 | 0.71 | 0.08 | asserted 1.00 |
| s4 | This and other arguments identify the N=3 superconformal field theory dual to M-theory compactified on AdS_4 x N^{0,1,0}. | result 0.76 | 0.83 | 0.63 | asserted 0.94 |
| s5 | It is an N=3 gauge theory with SU(N) x SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern Simons interaction. | result 0.90 | 0.66 | 0.17 | asserted 1.00 |
| s6 | The AdS/CFT correspondence can be directly verified using the recently worked out Kaluza Klein spectrum of N^{0,1,0} and we find a perfect match. | result 0.95 | 0.92 | 0.12 | asserted 1.00 |
| s7 | We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin 3/2 N=3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N=4 theory. | result 0.73 | 0.93 | 0.04 | speculative 0.47 |
| s8 | We investigate this intriguing and inspiring feature in a separate paper. | future work 1.00 | 0.29 | 0.02 | asserted 0.64 |
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Original abstract
In this paper we investigate three-dimensional superconformal gauge theories with N=3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three dimensional N=3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N=2 theories. When the superconformal field theory is realized on the world-volume of an M2-brane such superfield ring is the counterpart of the ring defined by the algebraic geometry of the 8-dimensional cone transverse to the brane. This and other arguments identify the N=3 superconformal field theory dual to M-theory compactified on AdS_4 x N^{0,1,0}. It is an N=3 gauge theory with SU(N) x SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern Simons interaction. The AdS/CFT correspondence can be directly verified using the recently worked out Kaluza Klein spectrum of N^{0,1,0} and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin 3/2 N=3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N=4 theory. We investigate this intriguing and inspiring feature in a separate paper.
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20 arXiv papers cite this in 30 sentences
Papers citing it · 17 sentences without a confident label
Compares with it 1 paper
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[Similar Higgs branches also appear in the hyper-Kähler quotient description of the $d=3$, $=3$ CFT discussed in [ref] .] In other words, _V(crystal) = _H ×_H.
M2-brane Probe Dynamics and Toric Duality · Comparison with D-brane gauge theory · 0.80
Cites it as background 12 papers
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In this section we focus on the holographic dual of M-theory on $AdS_4 ×N^0,1,0/_k$ [ref] . $N^0,1,0$ is a homogeneous Sasakian of dimension seven and defined as the coset $(3)/(1)$.
Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces · The $N^0,1,0/_k$ theory · 0.93
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In this section we focus on the holographic dual of M-theory on $AdS_4 ×N^0,1,0/_k$ [ref] . $N^0,1,0$ is a homogeneous Sasakian of dimension seven and defined as the coset $(3)/(1)$.
Black hole microstates and supersymmetric localization · The index at large $N$ · 0.91
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Previous attempts to find dual pairs have focused on Yang-Mills theories flowing in the IR to superconformal fixed points [ref] .
Tilings, Chern-Simons Theories and M2 Branes · Introduction · 0.96
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