Recently, the bi-local fields attract the interest in studying the duality between O(N) vector model and a higher-spin gauge theory in AdS spacetime. In those theories, the bi-local fields are realized as collective one’s of the O(N ) vector fields, which are the source of higher-spin bulk fields. Historically, the bi-local fields are introduced as a candidate of non-local fields by Yukawa. Today, Yukawa’s bi-local fields are understood from a viewpoint of relativistic two-particle bound systems, the bi-local systems. We study the relation between the bi-local collective fields out of higher-spin bulk fields and the fields out of the bi-local systems embedded in AdS5 spacetime with warped metric. It is shown that the effective spring constant of the bi-local system depends on the brane, on which the bi-local system is located. In particular, a bi-local system with vanishing spring constant, which is similar to the bi-local collective fields, can be realized on a low-energy IR brane.
AdS-CFT Correspondence Field Theories in Higher Dimensions Higher Spin Gravity
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S. Abe and S. Naka, Bi-local model with additional internal dynamical variables and interaction with external fields, Prog . Theor. Phys.87 (1992) 469.ADSCrossRefGoogle Scholar
N. Kanda and S. Naka, Bi-local field in gravitational shockwave background, PTEP2015 (2015) 033B10 [arXiv:1410.4014] [INSPIRE].
B.S. DeWitt, Dynamical theory of groups and fields, in Relativity, group and topology, lectures delivered at Les Houches 1963, Gordon and Breach, Science Publishers Inc., Philadelphi U.S.A. (1964).Google Scholar