Double-trace deformations of conformal correlations

Giombi, Simone; Kirilin, V.P.; Perlmutter, Eric

doi:10.1007/jhep02(2018)175

Cited by 31 publications

(84 citation statements)

References 69 publications

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“…This fact was pointed out, e.g., in [32,42,43], and can be understood in two steps as follows. Firstly…”

Section: Conformal Partial Wavesmentioning

confidence: 94%

Recursion relations in Witten diagrams and conformal partial waves

Zhou

2019

J. High Energ. Phys.

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We revisit the problem of performing conformal block decomposition of exchange Witten diagrams in the crossed channel. Using properties of conformal blocks and Witten diagrams, we discover infinitely many linear relations among the crossed channel decomposition coefficients. These relations allow us to formulate a recursive algorithm that solves the decomposition coefficients in terms of certain seed coefficients. In one dimensional CFTs, the seed coefficient is the decomposition coefficient of the double-trace operator with the lowest conformal dimension. In higher dimensions, the seed coefficients are the coefficients of the double-trace operators with the minimal conformal twist. We also discuss the conformal block decomposition of a generic contact Witten diagram with any number of derivatives. As a byproduct of our analysis, we obtain a similar recursive algorithm for decomposing conformal partial waves in the crossed channel.

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“…This fact was pointed out, e.g., in [32,42,43], and can be understood in two steps as follows. Firstly…”

Section: Conformal Partial Wavesmentioning

confidence: 94%

Recursion relations in Witten diagrams and conformal partial waves

Zhou

2019

J. High Energ. Phys.

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“…For example, while VOA data does not depend on marginal couplings, it is not generally clear whether a large c limit of a sequence of SCFTs also has large ∆ gap . 25 Therefore, checking whether (B.12) is satisfied in an infinitely-stronglygenerated VOA with |c 2d | → ∞ may be a useful practical tool for addressing that question, by suggesting that it should be associated to an SCFT.…”

Section: B2 Chiral Algebra Corollarymentioning

confidence: 99%

“…13) Bulk reconstruction from large N bootstrap: There has been recent progress in building up AdS amplitudes from large N bootstrap, or bootstrap-inspired, methods. This is true both for "bottom-up" ingredients such as Witten diagrams [2,[20][21][22][23][24][25], and topdown, complete amplitudes in string/M-theory at both genus zero [26][27][28][29][30][31][32][33][34] and genus one [35][36][37][38][39][40][41][42][43]. It is natural to apply these insights to more abstract investigations of the AdS landscape.These topics invite many questions.…”

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confidence: 99%

Growing extra dimensions in AdS/CFT

Alday

Perlmutter

2019

J. High Energ. Phys.

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What is the dimension of spacetime? We address this question in the context of the AdS/CFT Correspondence. We give a prescription for computing the number of large bulk dimensions, D, from strongly-coupled CFT d data, where "large" means parametrically of order the AdS scale. The idea is that unitarity of 1-loop AdS amplitudes, dual to non-planar CFT correlators, fixes D in terms of tree-level data. We make this observation rigorous by deriving a positive-definite sum rule for the 1-loop doublediscontinuity in the flat space/bulk-point limit. This enables us to prove an array of AdS/CFT folklore, and to infer new properties of large N CFTs at strong coupling that ensure consistency of emergent large extra dimensions with string/M-theory. We discover an OPE universality at the string scale: to leading order in large N , heavyheavy-light three-point functions, with heavy operators that are parametrically lighter than a power of N , are linear in the heavy conformal dimension. We explore its consequences for supersymmetric CFTs and explain how emergent large extra dimensions relate to a Sublattice Weak Gravity Conjecture for CFTs. Lastly, we conjecture, building on a claim of [1], that any CFT with large higher-spin gap and no global symmetries has a holographic hierarchy: D = d + 1.2) String/M-theory landscape beyond supergravity: What is the landscape of consistent AdS vacua? This question is old because it is challenging. The scales in the problem are the AdS scale L, the KK scale L M (where M is some internal manifold), the Planck scale ℓ p , and (in string theory) the string scale ℓ s . Reliable bulk construction of scale-separated AdS vacua (L M ≪ L) in string theory requires control at finite α ′ and, perhaps, at finite g s . This is not currently possible without resorting to parametric effective field theory arguments, and/or assumptions about the structure of α ′ perturbation theory and/or backreaction of sources, which existing works all employ in some way. 13) Bulk reconstruction from large N bootstrap: There has been recent progress in building up AdS amplitudes from large N bootstrap, or bootstrap-inspired, methods. This is true both for "bottom-up" ingredients such as Witten diagrams [2,[20][21][22][23][24][25], and topdown, complete amplitudes in string/M-theory at both genus zero [26][27][28][29][30][31][32][33][34] and genus one [35][36][37][38][39][40][41][42][43]. It is natural to apply these insights to more abstract investigations of the AdS landscape.These topics invite many questions. We will answer the following one:Define D as the number of "large" bulk dimensions, of order the AdS scale. Given the local operator data of a large ∆ gap CFT to leading order in 1/c, what is D?Unlike other questions in the realm of holographic spacetime, this is not possible to answer classically using a finite number of fields: consistent truncations exist.On the other hand, quantum effects in AdS can tell the difference between D dimensions and d + 1 dimensions. Our key idea is that AdS loop amplitudes are se...

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“…It was shown in [21] that calculations of Witten diagrams essentially simplify when they include "extremal" vertexes [35] that means fulfillment of "extremal" relation (3) ∆ ψ 1 = ∆ ψ 2 + ∆ ψ 3 between conformal dimensions of three interacting fields. This in turn means that conformal operator of the first field is the composite operator which is a product of two other operators, see discussion in the Introduction.…”

Section: O(n ) Symmetric Model With Composite Scalarmentioning

confidence: 99%

“…in the RHS of (24) diverges as Γ 2 (0). To compensate this divergence it is necessary to apply a regularization proposed in [21] which is different from the one in (25). In [21] the norm-invariant coupling constant was introduced:…”

Section: O(n ) Symmetric Model With Composite Scalarmentioning

confidence: 99%

“Old” conformal bootstrap on AdS: O(N) symmetric scalar model

Altshuler

2020

Int. J. Mod. Phys. A

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Bootstrap equations for conformal correlators that mimic the early theory of conformal bootstrap are written down in frames of the AdS/CFT approach. The simplified version of these equations, that may be justified if Schwinger-Keldysh formalism is used in AdS/CFT instead of conventional Feynman-Witten diagrams technique, permits to calculate values of conformal dimensions in the O(N) symmetric model with conformal or composite Habbard-Stratonovich field.

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Double-trace deformations of conformal correlations

Cited by 31 publications

References 69 publications

Recursion relations in Witten diagrams and conformal partial waves

Recursion relations in Witten diagrams and conformal partial waves

Growing extra dimensions in AdS/CFT

“Old” conformal bootstrap on AdS: O(N) symmetric scalar model

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