Perturbative and non-perturbative aspects in vector model/higher spin duality

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 46; no. 21; pp. 214005 - 18
• Main Authors: Jevicki, Antal, Jin, Kewang, Ye, Qibin
• Format: Journal Article
• Language: English
• Published: IOP Publishing 31.05.2013
• Subjects: Constants; Gravitation; Mathematical analysis; Mathematical models; Nonlinearity; Pauli exclusion principle; Three dimensional models; Transformations; Vectors (mathematics)
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/46/21/214005

We review some recent work on AdS/CFT duality involving the 3D O(N) vector model and AdS4 higher spin gravity. Our construction is based on bi-local collective field theory which provides an off-shell formulation of higher spin gravity with G = 1 N playing the role of a coupling constant. Consequently, perturbative and non-perturbative issues of the theory can be studied. For the correspondence based on free CFTs we discuss the nature of bulk 1 N interactions through an S-matrix which is argued to be equal to 1 (Coleman-Mandula theorem). As a consequence in this class of theories nonlinearities are removable, through a nonlinear field transformation which we show at the exact level. We also describe a geometric (Kähler space) framework for the bi-local theory which applies equally simply to Sp(2N) fermions and the de Sitter correspondence. We discuss in this framework the structure and size of the bi-local Hilbert space and the implementation of (finite N) exclusion principle. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Higher spin theories and holography'.