Universality of long-distance AdS physics from the CFT bootstrap

By A. Fitzpatrick, Jared Kaplan, Matthew T. Walters. 2014

465 citations recorded by the source corpus.

A bstractWe begin by explicating a recent proof of the cluster decomposition principle in AdS≥4 from the CFT≥3 bootstrap. The CFT argument also computes the leading interactions between distant objects in AdS≥4, and we confirm the universal agreement between the CFT bootstrap and AdS gravity in the semi-classical limit.We proceed to study the generalization to CFT2, which requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit. We compute these blocks in a semiclassical, large central charge approximation, and use them to prove a suitably modified theorem. In particular, from the d = 2 bootstrap we prove the existence of large spin operators with fixed ‘anomalous dimensions’ indicative of the presence of deficit angles in AdS3. As we approach the threshold for the BTZ black hole, interpreted as a CFT2 scaling dimension, the twist spectrum of large spin operators becomes dense.Due to the exchange of the Virasoro identity block, primary states above the BTZ threshold mimic a thermal background for light operators. We derive the BTZ quasinormal modes, and we use the bootstrap equation to prove that the twist spectrum is dense. Corrections to thermality could be obtained from a more refined computation of the Virasoro conformal blocks.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/20c92210716a907e08b18c58779da9b511bbd009

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Citations in the corpus

Bootstrapping mixed correlators in the 3D Ising model (2014, background): “The conformal bootstrap [1, 2] in D > 2 dimensions has produced remarkable results, including numerical bounds on operator dimensions and OPE coefficients [3–29], analytical constraints [30–36], and recently a precise conjecture for the Z2-even spectrum of the 3D Ising model [23].”
A proof of the conformal collider bounds (2016, background): “An especially exciting question is the quantum origin of universal features of gravitational interactions, such as causality, (non-)locality and attractiveness [16{18, 32, 76{78].”
Black hole collapse in the 1/c expansion (2016, methodology): “A method to solve the monodromy problem in this limit, with a finite number n of background insertions, was introduced in [11].”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, result): “The ideas developed in this paper originated by thinking about the bulk representation of Virasoro conformal blocks in AdS3/CFT2, based on recent results in this direction [28–33].”
Low-dimensional de Sitter quantum gravity (2019, methodology): “The model arising from Euclidean AdS3 computes Virasoro identity blocks [36, 103–109], and provides another method to calculate Virasoro Wilson lines [110–115].”
Bootstrapping the O(N) archipelago (2015, unknown): “In recent years great progress has been made in the conformal bootstrap in d > 2, including rigorous bounds on operator dimensions and operator product expansion (OPE) coefficients [3–32], analytical constraints [33–45], and methods for approximate direct solutions to the bootstrap [46–49], includin”
Universal spectrum of 2d conformal field theory in the large c limit (2014, result): “This is similar in spirit to recent efforts to derive universal features of entanglement entropy [12–15] and gravitational interactions [16] at large c.”
Holographic entanglement entropy from 2d CFT: heavy states and local quenches (2014, methodology): “In a general large-c CFT, the match to bulk results discussed in [34] holds only at very high energies, but in sparse CFTs where our approximations apply for all z, many of the results of [34] should hold at all frequencies.”
Semiclassical Virasoro blocks from AdS3 gravity (2015, methodology): “Partial results on bulk derivations of Virasoro blocks are already known [17–19], and we will incorporate and reproduce them here.”
Spinning AdS propagators (2014, result): “which agrees with the results of [52, 53, 54] (in particular see formula (B.”
A theory of reparameterizations for AdS3 gravity (2018, background): “Our results reproduce those of [68, 69], including the “quantum” corrections of [18, 19].”
Quantum entanglement of localized excited states at finite temperature (2014, unknown): “As pointed out in the remarkable paper [46], the 4-pt function of two heavy operators OB with two light operatorsOA equals a thermal 2-pt function in the large c limit as follows:”
Virasoro conformal blocks and thermality from classical background fields (2015, unknown): “The results in [25] apply to a di(cid:11)erent regime of parameter space, so let us clarify how those results relate to the present ones.”
Bounding the space of holographic CFTs with chaos (2016, background): “In this semiclassical limit, the Virasoro vacuum block is [91]”