Abstract
We consider the relevance of a collective field theory description for the AdS/CFT correspondence. Collective field theory performs a systematic reorganization of the degrees of freedom of a (non-gravitational) field theory, replacing the original loop expansion parameter ℏ with 1/N. Collective fields are over complete signalling a redundancy inherent in the theory. We propose that this over completeness is the mechanism by which one arrives at a holographic description, to be identified with the gravity dual. We find evidence for this by studying the redundancy of the collective field theory, showing that degrees of freedom in the bulk can be expressed as a linear combination of degrees of freedom contained in an arbitrarily small neighbourhood of the boundary.
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Acknowledgments
This research is supported by a start up research fund of Huzhou University, a Zhejiang Province talent award and by a Changjiang Scholar award. The author would like to thank the Isaac Newton Institute for Mathematical Schiences for support and hospitality during the programme “Black holes: bridges between number theory and holographic quantum information” when work on this paper was completed. This work was supported by EPSRC Grant Number EP/R014604/1. We thank Suvrat Raju for helpful correspondence on [14]. We thank Cameron Beetar, Garry Kemp, Jaco Van Zyl and especially Antal Jevicki for very useful discussions on the subject of this paper.
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de Mello Koch, R. Gravitational dynamics from collective field theory. J. High Energ. Phys. 2023, 151 (2023). https://doi.org/10.1007/JHEP10(2023)151
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DOI: https://doi.org/10.1007/JHEP10(2023)151