1/N and Loop Corrections in Higher Spin AdS_4/CFT_3 Duality

Abstract

We consider the question of loop corrections (i.e. 1/N) in the vector model/higher spin duality following the recent work of Giombi and Klebanov. The purpose of this paper is to gain further more precise comparison between the two sides of the duality. For CFTs given by 3d O(N) or U(N) vector models we evaluate the leading and one loop partition functions in a variety of geometries. Our calculations are performed in the scheme of collective field theory which was seen in earlier studies to represent a bulk description of Vasiliev higher spin theory. The calculations presented provide data for comparison of small fluctuation determinants giving further evidence for the one-to-one bulk identification between the bi-local and the AdS picture. They also offer insight into the identification of coupling constants G and 1/N of the two descriptions for models based on O(N) symmetry.

17 pages

References in corpus (4)

• Hadronic Spectra and Light-Front Wavefunctions in Holographic QCD
• AdS_4/CFT_3 Construction from Collective Fields
• Higher Spin AdS${}_{d+1}$/CFT${}_d$ at One Loop
• Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary

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• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• TASI Lectures on the Higher Spin - CFT duality
• Canonical Formulation of $O(N)$ Vector/Higher Spin Correspondence
• On the Holography of Free Yang-Mills
• Bi-Local Holography in the SYK Model: Perturbations
• Near Conformal Perturbation Theory in SYK Type Models
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
• Quantum Error Correction and Holographic Information from Bilocal Holography
• Holographic computation of quantum corrections to the bulk cosmological constant