How to succeed at holographic correlators without really trying

Rastelli, Leonardo; Zhou, Xinan

doi:10.1007/jhep04(2018)014

Cited by 211 publications

(650 citation statements)

References 110 publications

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“…In particular, these works discussed the case where the light operator is a simple chiral primary operator (see (2.7)): [22] focussed on the case where the heavy state is made out of many copies of the same supergravity mode and found that the 4-point correlator at the gravity point matched precisely the orbifold theory result, suggesting that there is a non-renormalisation theorem for this type of correlators; [23] considered a more complicated heavy operator made out of two types of supergravity modes. This second case provides the first explicit example of a dynamical HHLL correlator, where the result in the SCFT strong coupling region is radically different from the one valid at 2 There is a vast literature on holographic four point correlators in the context of the AdS 5 /N = 4 SYM duality; see [18] for a detailed discussion of a modern approach to the problem and references to original papers. Here we focus on the AdS 3 /CFT 2 case and the HHLL correlators of which much less is known.…”

Section: Introductionmentioning

confidence: 95%

Unitary 4-point correlators from classical geometries

et al. 2018

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We compute correlators of two heavy and two light operators in the strong coupling and large c limit of the D1D5 CFT which is dual to weakly coupled AdS 3 gravity. The light operators have dimension two and are scalar descendants of the chiral primaries considered in arXiv:1705.09250, while the heavy operators belong to an ensemble of Ramond-Ramond ground states. We derive a general expression for these correlators when the heavy states in the ensemble are close to the maximally spinning ground state. For a particular family of heavy states we also provide a result valid for any value of the spin. In all cases we find that the correlators depend non-trivially on the CFT moduli and are not determined by the symmetries of the theory; however, they have the properties expected for correlators among pure states in a unitary theory, in particular they do not decay at large Lorentzian times.

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Section: Introductionmentioning

confidence: 95%

Unitary 4-point correlators from classical geometries

et al. 2018

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“…From (3.22), and the known expressions for the subleading corrections to the conformal blocks, we can find the function S(v, u) order by order in v. Unfortunately we have not been able to find a closed form for it in position space, instead finding a closed form in Mellin space. We follow the conventions in [39], borrowing the language to describe holographic correlators. For a correlator of identical external operators of dimension ∆ ϕ , we define the Mellin amplitude M(s, t) by…”

Section: Mellin Amplitudementioning

confidence: 99%

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

Alday

Henriksson

Loon

2020

J. High Energ. Phys.

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We apply the methods of modern analytic bootstrap to the critical O(N ) model in a 1/N expansion. At infinite N the model possesses higher spin symmetry which is weakly broken as we turn on 1/N . By studying consistency conditions for the correlator of four fundamental fields we derive the CFT-data for all the (broken) currents to order 1/N , and the CFT-data for the non-singlet currents to order 1/N 2 . To order 1/N our results are in perfect agreement with those in the literature. To order 1/N 2 we reproduce known results for anomalous dimensions and obtain a variety of new results for structure constants, including the global symmetry central charge C J to this order.

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“…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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How to succeed at holographic correlators without really trying

Cited by 211 publications

References 110 publications

Unitary 4-point correlators from classical geometries

Unitary 4-point correlators from classical geometries

An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2

Growing extra dimensions in AdS/CFT

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