Large N bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction

Mulokwe, Mbavhalelo; Rodrigues, J. P.

doi:10.1007/jhep11(2018)047

Cited by 8 publications

(6 citation statements)

References 39 publications

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“…In this section we discuss the deformation of the free scalar CFT by a ( I |φ I | 2 ) 2 term, which in the bi-local theory is a double-trace deformation λN G 2 (x, x), and the critical theory that it leads to in the low-energy (λ → ∞) limit for 2 < d < 4. We start by reviewing the doubletrace deformation of the free U (N ) or O(N ) CFT, following [64][65][66][67]. We will then discuss the bulk dual of the critical theory, using the off-shell mapping of η(x, x) to the boundary limit of Φ 0 (x, z) (4.45).…”

Section: The Double Trace Deformation and The Critical Theorymentioning

confidence: 99%

A Derivation of AdS/CFT for Vector Models

Aharony,

Chester,

Urbach

2020

Preprint

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We explicitly rewrite the path integral for the free or critical O(N ) (or U (N )) bosonic vector models in d space-time dimensions as a path integral over fields (including massless high-spin fields) living on (d + 1)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large N limit to Vasiliev's classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1/N expansion, but in principle can be extended also to finite N theories, where extra constraints on products of bulk fields need to be taken into account.

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Section: The Double Trace Deformation and The Critical Theorymentioning

confidence: 99%

A Derivation of AdS/CFT for Vector Models

Aharony,

Chester,

Urbach

2020

Preprint

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“…We follow the (λ = 0) case, noting the fact that the discussion of the IR fixed point case is essentially the same (with only a boundary condition change for the lowest mode). A recent on-shell discussion of IR bi-local states is given in [36].…”

Section: Bi-local Propagatormentioning

confidence: 99%

AdS maps and diagrams of bi-local holography

Koch

Jevicki

Suzuki

et al. 2019

J. High Energ. Phys.

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We present in detail the basic ingredients contained in bi-local holography, representing a constructive scheme for reconstructing AdS bulk theories in Vectorial/AdS duality. Explicit Mapping to bulk AdS and higher spin fields is seen to be given by a double Fourier transform. All order interactions are explicitly specified through the collective action. This generates bulk Feynman (Witten) diagrams (at tree and loop level). We give details of the four-point case evaluation. It is noted that the bi-local construction goes beyond the assumptions in various discussions of non-locality. λ∆,s ≈ 1 4 (∆ 2 − s 2 ) 2 .(3.21)

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“…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

J. High Energ. Phys.

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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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Large N bilocals at the infrared fixed point of the three dimensional O(N) invariant vector theory with a quartic interaction

Cited by 8 publications

References 39 publications

A Derivation of AdS/CFT for Vector Models

A Derivation of AdS/CFT for Vector Models

AdS maps and diagrams of bi-local holography

Gravitational dynamics from collective field theory

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