ABJ Quadrality

Abstract

We study physical consequences of adding orientifolds to the ABJ triality, which is among 3d N=6 superconformal Chern-Simons theory known as ABJ theory, type IIA string in AdS_4 x CP^3 and N=6 supersymmetric (SUSY) Vasiliev higher spin theory in AdS_4. After adding the orientifolds, it is known that the gauge group of the ABJ theory becomes O(N_1)xUSp(2N_2) while the background of the string theory is replaced by AdS_4 x CP^3/Z_2, and the supersymmetries in the both theories reduce to N=5. We propose that adding the orientifolds to the N=6 Vasiliev theory leads to N=5 SUSY Vasiliev theory. It turns out that the N=5 case is more involved because there are two formulations of the N=5 Vasiliev theory with either O or USp internal symmetry. We show that the two N=5 Vasiliev theories can be understood as certain projections of the N=6 Vasiliev theory, which we identify with the orientifold projections in the Vasiliev theory. We conjecture that the O(N_1)xUSp(2N_2) ABJ theory has the two vector model like limits: N_2 >> N_1 and N_1 >> N_2 which correspond to the semi-classical N=5 Vasiliev theories with O(N_1) and USp(2N_2) internal symmetries respectively. These correspondences together with the standard AdS/CFT correspondence comprise the ABJ quadrality among the N=5 ABJ theory, string/M-theory and two N=5 Vasliev theories. We provide a precise holographic dictionary for the correspondences by comparing correlation functions of stress tensor and flavor currents. Our conjecture is supported by various evidence such as agreements of the spectra, one-loop free energies and SUSY enhancement on the both sides. We also predict the leading free energy of the N=5 Vasiliev theory from the CFT side. As a byproduct, we give a derivation of the relation between the parity violating phase in the N=6 Vasiliev theory and the parameters in the N=6 ABJ theory, which was conjectured in arXiv:1207.4485.

38+15 pages, 4 figures; v2: minor corrections

References in corpus (17)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
• Seiberg Duality in Chern-Simons Theory
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Higher Spins in AdS and Twistorial Holography
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Exact results on ABJ theory and the refined topological string
• Higher spin AdS_3 holography with extended supersymmetry
• Seiberg-like duality in three dimensions for orthogonal gauge groups
• TASI Lectures on the Higher Spin - CFT duality
• Topological Chern-Simons/Matter Theories
• Test of the local form of higher-spin equations via AdS/CFT
• Correlation Functions in $\omega$-Deformed N=6 Supergravity
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• One-loop supergravity on ${\mathrm{AdS}}_4\times S^7/{\mathbb{Z}}_k$ and comparison with ABJM theory