Rings of short N=3 superfields in three dimensions and M-theory on AdS_4 x N^{0,1,0}

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.

23 pages, LaTex

References in corpus (9)

• Large N Field Theories, String Theory and Gravity
• CFT's From Calabi-Yau Four-folds
• Spectrum of Type IIB Supergravity on AdS_5 x T^{11}: Predictions on N = 1 SCFT's
• 3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3
• The structure of N=3 multiplets in AdS_4 and the complete Osp(3|4) X SU(3) spectrum of M-theory on AdS_4 X N^{010}
• Osp(N|4) supermultiplets as conformal superfields on \partial AdS_4 and the generic form of N=2, D=3 gauge theories
• M Theory on the Stiefel manifold and 3d Conformal Field Theories
• Shadow multiplets in AdS_4/CFT_3 and the super-Higgs mechanism: hints of new shadow supergravities
• Conformal primaries of OSp(8/4,R) and BPS states in AdS4

Cited by in corpus (41)

• Tilings, Chern-Simons Theories and M2 Branes
• Brane Tilings and M2 Branes
• Brane Tilings and Their Applications
• Notes on adding D6 branes wrapping RP3 in AdS4 x CP3
• Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
• RG flows from Spin(7), CY 4-fold and HK manifolds to AdS, Penrose limits and pp waves
• On N=1,2,4 Higher Spin Gauge Theories in Four Dimensions
• Tri-Sasakian consistent reduction
• Marginal Deformations of Field Theories with AdS_4 Duals
• N=2 solutions of massive type IIA and their Chern-Simons duals
• The Squashed, Stretched, and Warped Gets Perturbed
• Superconformal field theories from crystal lattices
• M2-brane Probe Dynamics and Toric Duality
• Shadow multiplets in AdS_4/CFT_3 and the super-Higgs mechanism: hints of new shadow supergravities
• Supersymmetric Janus solutions in four-dimensional N=3 gauged supergravity
• Hairy Black Holes and Duality in an Extended Supergravity Model
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• AdS/CFT with Tri-Sasakian Manifolds
• Supersymmetric deformations of 3D SCFTs from tri-sasakian truncation
• Eschenburg space as gravity dual of flavored N=4 Chern-Simons-matter theory
• Holographic RG flows in N=3 Chern-Simons-Matter theory from N=3 4D gauged supergravity
• Evidence for the Holographic dual of $\mathcal{N}=3$ Solution in Massive Type IIA
• Gaugings of four-dimensional N=3 supergravity and AdS4/CFT3 holography
• M5-brane Defect and QHE in AdS_4 x N(1,1)/N=3 SCFT
• Twisted tori and fluxes: a no go theorem for Lie groups of weak G_2 holonomy
• New $Ad{S}_4\times X_7$ Geometries with $\mathcal{N}=6$ in M Theory
• Black hole microstates and supersymmetric localization
• Other Squashing Deformation and N=3 Superconformal Chern-Simons Gauge Theory
• Supersymmetric AdS${}_2\times {\Sigma }_2$ solutions from tri-sasakian truncation
• Constrained Supermanifolds for AdS M-Theory Backgrounds
• The Kähler Quotient Resolution of ${\mathbb{C}}^3/\Gamma$ singularities, the McKay correspondence and D=3 $\mathcal{N}=2$ Chern-Simons gauge theories
• Penrose Limit of AdS_4 x N^{0,1,0} and N=3 Gauge Theory
• On perturbative instability of Pope-Warner solutions on Sasaki-Einstein manifolds
• Crepant Resolutions of ${\mathbb{C}}^3/{\mathbb{Z}}_4$ and the Generalized Kronheimer Construction (in view of the Gauge/Gravity Correspondence)
• The Integral Form of D=3 Chern-Simons Theories Probing ${\mathbb{C}}^n/\Gamma$ Singularities
• Gauged $\mathcal{N}=3,D=4$ Supergravity: a new web of marginally connected vacua
• Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories
• Dualities from large N orbifold equivalence in Chern-Simons-matter theories with flavor
• New Janus interfaces from four-dimensional N=3 gauged supergravity
• The ${\mathcal{N}}_3=3\to {\mathcal{N}}_3=4$ enhancement of Super Chern-Simons theories in $D=3$, Calabi HyperKähler metrics and M2-branes on the $\mathcal{C}({\mathrm{N}}^{0,1,0})$ conifold