Constructing the bulk at the critical point of three-dimensional large N vector theories

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.

“…For recent discussions of holography using the unequal time bilocal see [45][46][47] and for the holography of the IR fixed point see [48,49].…”

Section: Jhep10(2023)151mentioning

confidence: 99%

Gravitational dynamics from collective field theory

de Mello Koch

2023

“…Although we do not need it for what follows, note that bilocal holography has been studied for the interacting IR fixed point of the O(N ) model in [41,42] and the bilocal holography of the thermofield double has been constructed in [33,43,44].…”

Section: Jhep12(2022)095mentioning

confidence: 99%

Holography of information in AdS/CFT

Koch

Kemp

2022

The principle of the holography of information states that in a theory of quantum gravity a copy of all the information available on a Cauchy slice is also available near the boundary of the Cauchy slice. This redundancy in the theory is already present at low energy. In the context of the AdS/CFT correspondence, this principle can be translated into a statement about the dual conformal field theory. We carry out this translation and demonstrate that the principle of the holography of information holds in bilocal holography.

“…This change of coordinates is highly non-trivial and the correctness of this step was verified by showing that the complete set of generators of the conformal field theory are mapped into those of the higher spin gravity [19]. Bilocal holopgraphy has been developed in a number of interesting directions [20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Bilocal holography and locality in the bulk

de Mello Koch,

Kemp,

Van Zyl

2024

Bilocal holography provides a constructive approach to the vector model/higher spin gravity duality. It has two ingredients: a change of field variables and a change of space time coordinates. The change of field variables ensures that the loop expansion parameter becomes $$ \frac{1}{N} $$ 1 N . The change of coordinates solves the Clebsch-Gordan problem of moving from the tensor product basis (in which the collective bilocal field is written) to the direct sum basis (appropriate for the description of the gravity fields). We argue that the change of space time coordinates can be deduced by requiring that operators constructed in the bilocal collective field theory are dual to local operators in the AdS bulk.