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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
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.
