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Multitrace Deformations of Vector and Adjoint Theories and their Holographic Duals
High Energy Physics - Theory · Submitted 4 Nov 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.
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The abstract, sentence by sentence
We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. | contribution 0.99 | 0.91 | 0.08 | asserted 1.00 |
| s1 | In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. | contribution 0.62 | 0.87 | 0.16 | asserted 1.00 |
| s2 | We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. | result 0.54 | 0.63 | 0.11 | asserted 0.83 |
| s3 | We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. | result 0.98 | 0.81 | 0.12 | asserted 1.00 |
| s4 | We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. | contribution 0.83 | 0.92 | 0.23 | asserted 1.00 |
| s5 | The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT. | interpretation 1.00 | 0.61 | 0.42 | hedged possibility 1.00 |
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The paper
Original abstract
We present general methods to study the effect of multitrace deformations in conformal theories admitting holographic duals in Anti de Sitter space. In particular, we analyse the case that these deformations introduce an instability both in the bulk AdS space and in the boundary CFT. We also argue that multitrace deformations of the O(N) linear sigma model in three dimensions correspond to nontrivial time-dependent backgrounds in certain theories of infinitely many interacting massless fields on AdS_4, proposed years ago by Fradkin and Vasiliev. We point out that the phase diagram of a truly marginal large-N deformation has an infrared limit in which only an O(N) singlet field survives. We draw from this case lessons on the full string-theoretical interpretation of instabilities of the dual boundary theory and exhibit a toy model that resolves the instability of the O(N) model, generated by a marginal multitrace deformation. The resolution suggests that the instability may not survive in an appropriate UV completion of the CFT.
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References
How the literature uses it
23 arXiv papers cite this in 39 sentences
Papers citing it · 25 sentences without a confident label
Compares with it 1 paper
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[ This conclusion might at first sight appear different from that reached in [ref] .
A multitrace deformation of ABJM theory · The $O(N)$ vector model · 0.90
Cites it as support 1 paper
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Furthermore, we demonstrate that \(W\)-freedom, which modifies the bulk boundary conditions, corresponds to a multi-trace deformation in the boundary theory [ref] (and for a systematic treatment of multi-trace deformations see also [ref] and also [ref] ).
Freelance Holography, Part I: Setting Boundary Conditions Free in Gauge/Gravity Correspondence · Introduction · 0.97
Cites it as background 11 papers
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See [ref] for a recent discussion.
A multitrace deformation of ABJM theory · The $O(N)$ vector model · 0.87
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The interesting case is the tri-critical model, which includes just the kinetic term and a term proportional to a triple-trace deformation of it; see for instance [ref] .
A Truncation of 11-Dimensional Supergravity for Fubini-Like Instantons in AdS_4/CFT_3 · Boundary Field Theory Duals · 0.82
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The properties of these solutions and their duals were further explored in [ref] .
Particle Production near an AdS Crunch · Introduction · 0.92
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