Holography from Conformal Field Theory

By Idse Heemskerk, J. Penedones, J. Polchinski, J. Sully. 2009

867 citations recorded by the source corpus.

The locality of bulk physics at distances below the AdS length scale is one of the remarkable aspects of AdS/CFT duality, and one of the least tested. It requires that the AdS radius be large compared to the Planck length and the string length. In the CFT this implies a large-N expansion and a gap in the spectum of anomalous dimensions. We conjecture that the implication also runs in the other direction, so that any CFT with a large-N expansion and a large gap has a local bulk dual. For an abstract CFT we formulate the consistency conditions, most notably crossing symmetry, and show that the conjecture is true in a broad range of CFT's, to first nontrivial order in 1/N-2: in any CFT with a gap and a large-N expansion, the four-point correlator is generated via the AdS/CFT dictionary from a local bulk interaction. We establish this result by a counting argument on each side, and also investigate various properties of some explicit solutions.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2858b9a38585bfbcbc3c8900317e36026b57c200

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Bounding the space of holographic CFTs with chaos (2016, methodology): “For example, one can easily show using the method of [59] that a λ(∂φv) (2)(∂φw) 2 term in the bulk Lagrangian contributes to the reduced amplitude as A(z, z) ⊃ λuv (1 + u+ v)D̄∆v+1,∆v+1,∆w+1,∆w+1(z, z) (3.”
Effective holographic theories for low-temperature condensed matter systems (2010, background): “In holographic CFTs, this implies the existence of a conserved global charge, and the duality between the associated conserved global current and a (massless) bulk gauge field.”
Gravitational S-matrix from CFT dispersion relations (2017, background): “ (but still nite) number of low spins can be aected. Such ambiguities are still constrained by crossing and thus correspond one-to-one to higher-dimensional operators in the bulk eective Lagrangian [2]. The fact that the tree-level supergravity result is determined, up to these ambiguities, by the s”
Radial Coordinates for Conformal Blocks (2013, background): “(19)We should also mention three different types of bootstrap analyses where analytic results could be obtained: [3] in the large N expansion; [11] for CFT in presence of a boundary; [13] and [14] in the Minkowski space near the light cone.”
The AdS/CFT correspondence (2014, background): “[105, 106], the latter recasting bulk S-matrix usefully in terms of a Mellin amplitude in CFT).”
Conformal Partial Waves: Further Mathematical Results (2011, neutral): “In two and four dimensions, with extensions possible for any even dimension, quite simple results have been found which have been found useful in bootstrap applications [8,9,10].”
A general proof of the quantum null energy condition (2017, background): “In order to have some control we would need to work with a QFT with a large-N limit and a gap in anomalous dimensions to the single trace higher spin fields [106].”
Convexity and liberation at large spin (2012, background): “The interested reader should consult [43,50] for interesting recent progress in this direction.”
Bootstrapping mixed correlators in the 3D Ising model (2014, methodology): “Finally, there is significant room for incorporating mixed correlators into general analytical studies of the bootstrap, both in the context of large N theories [30, 31] and in constraining the spectrum at large spin [32, 33].”
Holographic duality from random tensor networks (2016, background): “In the particular case when the bulk geometry is a hyperbolic space, the suppression of two-point correlations discussed here translates into the scaling dimension gap of boundary operators, which is known to be a required property for CFTs with gravity duals [23–25].”
The factorization problem in Jackiw-Teitelboim gravity (2018, background): “Most discussions of bulk physics in AdS/CFT focus on perturbative fields about a fixed background [1–8].”
Static patch solipsism: conformal symmetry of the de Sitter worldline (2011, background): “ues of the matrices (cf e.g. [57]). In the classical geometric limit, 20 the ‘stringy’ and thermalized o-diagonal excitations have become parametrically heavy compared to the diagonal modes (cf e.g. [58]). We can then imagine integrating out these modes to obtain an eective action for the eigenvalue”
Spinning conformal blocks (2011, background): “1 These ﬁelds, unlike the external scalars used so far [3–8], are conserved, so they have protected (and thus known) dimensions.”
Holographic Duality with a View Toward Many-Body Physics (2009, background): “This notion of locality in the extra dimension actually turns out to be much weaker than what we will find in AdS/CFT (as discussed recently in [23]), but it is a good hint.”
A bound on chaos (2015, background): “spirit of the speculation in [34] that a system with no light higher spin single trace states should have a gravity dual.”
Wormholes, emergent gauge fields, and the weak gravity conjecture (2015, background): “This is in some tension with the philosophy of “effective conformal field theory” advocated in [36–38], but it is not a contradiction with the validity of ECFT near the vacuum since we are”
Holographic and Wilsonian renormalization groups (2010, background): “hould then be possible to discuss more general subregions of the bulk, with some sort of equivalence principle relating dierent slicings. Possibly a more modest goal is to extend the results of Ref. [27], which found sucient conditions for local physics to emerge in the bulk. That approach of that p”
Looking for a bulk point (2015, background): “[10, 11]) assumed the singularity is present and showed how it could be used to extract the flat space scattering amplitude.”