The analytic bootstrap and AdS superhorizon locality

By A. Fitzpatrick, Jared Kaplan, David Poland, David Simmons-Duffin. 2012

541 citations recorded by the source corpus.

A bstractWe take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| ≪ |υ| < 1. We prove that every CFT with a scalar operator ϕ must contain infinite sequences of operators $ {{\mathcal{O}}_{{\tau, \ell }}} $ with twist approaching τ → 2Δϕ + 2n for each integer n as ℓ → ∞. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the ϕ × ϕ OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as ℓ → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f7e8c9655129247199b16f3ee4b1f09857db4c2e

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Citations in the corpus

Causality constraints in conformal field theory (2015, background): “This seems clear from the form of the t channel sum, but we do not know of a direct proof, so instead give an indirect argument using crossing symmetry and the results of [16, 17].”
The (2, 0) superconformal bootstrap (2015, background): “To get a handle on (C13) we follow [57,58] and consider the series expansion around z̄ 1⁄4 0.”
A general proof of the quantum null energy condition (2017, background): “This turns out to be a useful picture in any interacting CFT [54–56], and this was the original motivation for studying the lightcone limit in this context.”
Bootstrapping the O(N ) vector models (2013, background): “The representation as a sum over poles in ∆ may also be useful for making general analytic arguments (going beyond the large spin arguments of [55, 56]) in the context of the conformal bootstrap.”
The S-matrix bootstrap. Part I: QFT in AdS (2016, background): “J H E P 1 1 ( 2 0 1 7 ) 1 3 3 essential ingredients for the numerical bootstrap program [1–7], the analytic results at large spin [8, 9], and more recently the analysis of causality constraints [10–12].”
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].”
Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, unknown): “(See, however, [3, 44–48].”
Defects in conformal field theory (2016, methodology): “Besides specific examples, one more motivation for our work is provided by the recent progress in exploring the space of CFTs using the conformal bootstrap [36, 37, 38, 39, 40, 41, 42].”
Universality of long-distance AdS physics from the CFT bootstrap (2014, methodology): “In fact, the 2d Ising model provides an explicit counter-example [7].”
The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, background): “An interesting feature of this argument (not realized in [59, 60], but pointed out in [61]) is that it most naturally determines a function h(h) instead of τ(`).”
Virasoro conformal blocks and thermality from classical background fields (2015, unknown): “5.1 Far from the black hole: the lightcone OPE limit As discussed in [14, 15, 25], there is a lightcone OPE limit where correlation functions are dominated by the exchange of the identity Virasoro block.”
Carving out OPE space and precise O(2) model critical exponents (2019, unknown): “In the charge-0 sector, Nachtmann’s theorem [107–109], together with the existence of doubletwist operators [108, 110], implies that leading twists τ` for each even ` ≥ 4 satisfy 1 ≤ τ4 ≤ τ` ≤ 2∆φ ≈ 1.”
Spinning AdS propagators (2014, result): “which agrees with the results of [52, 53, 54] (in particular see formula (B.”