ABJ二次性
ABJ Quadrality
摘要：
我们研究了在3d N=6超共形Chern-Simons理论（简称ABJ理论）、AdS_4 x CP^3中的IIA型弦和AdS_4中的N=6超对称（SUSY）Vasiliev高自旋理论中加入定向折叠的物理后果。加入定向折叠后，ABJ理论的规范群变为O（N_1）xUSp（2N_2），而弦论的背景换成AdS_4 x CP^3/Z_2，两个理论的超对称性都降为N=5。我们建议，增加orientifolds到N=6 Vasiliev理论导致N=5 SUSY Vasiliev理论。事实证明，N=5的情况更复杂，因为N=5的瓦西里耶夫理论有两种形式，要么是O对称，要么是USp对称。我们表明，这两个N=5 Vasiliev理论可以理解为某些投影的N=6 Vasiliev理论，我们确定与orientifold预测Vasiliev理论。我们猜想O（N_1）xUSp（2N_2）ABJ理论具有两个类似于向量模型的极限：N_2 >> N_1和N_1 >> N_2，它们分别对应于具有O（N_1）和USp（2N_2）内部对称性的半经典N=5 Vasiliev理论.这些对应与标准的AdS/CFT对应一起构成了N=5 ABJ理论、弦/M理论和两个N=5 Vasliev理论中的ABJ四元性。通过比较应力张量和味流的关联函数，我们为对应关系提供了一个精确的全息字典。我们的猜想得到了各种证据的支持，如协议的光谱，单圈自由能和超对称性增强的双方。我们还从CFT的角度预测了N=5 Vasiliev理论的主导自由能。作为一个副产品，我们给出了在arXiv：1207.4485中描述的N =6 Vasiliev理论中宇称破坏相位与N=6 ABJ理论中参数之间的关系。
英文摘要：
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.
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