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The lightcone bootstrap and the spectrum of the 3d Ising CFT

Simmons-Duffin, David (2017) The lightcone bootstrap and the spectrum of the 3d Ising CFT. Journal of High Energy Physics, 2017 (3). Art. No. 086. ISSN 1029-8479.

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We compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2, RR ) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an asymptotic expansion in large spin, and suggest a strategy for going beyond the large spin limit. We carry out the first steps of this strategy for the 3d Ising CFT, deriving analytic approximations for the dimensions and OPE coefficients of several infinite families of operators in terms of the initial data {Δ_σ, Δ_ϵ, f_(σσϵ), f_(ϵϵϵ), c_T}. The analytic results agree with numerics to high precision for about 100 low-twist operators (correctly accounting for O(1) mixing effects between large-spin families). Plugging these results back into the crossing equations, we obtain approximate analytic constraints on the initial data.

Item Type:Article
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URLURL TypeDescription Paper
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2017 The Authors. Open Access. This article is distributed under the terms of the Creative Commons. Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received: February 14, 2017. Accepted: February 15, 2017. Published: March 15, 2017. I am grateful to Chris Beem, Simon Caron-Huot, Abhijit Gadde, Joanna Huey, Juan Maldacena, Eric Perlmutter, David Poland, Slava Rychkov, Douglas Stanford, and Balt van Rees for discussions. Thanks to Douglas Stanford and Slava Rychkov for comments on the draft. I am supported by DOE grant DE-SC0009988, a William D. Loughlin Membership at the Institute for Advanced Study, and Simons Foundation grant 488657 (Simons Collaboration on the Non-perturbative Bootstrap). The computations in this paper were run on the Hyperion computing cluster supported by the School of Natural Sciences Computing Staff at the Institute for Advanced Study.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0009988
Institute for Advanced StudyUNSPECIFIED
Simons Foundation488657
Subject Keywords:Conformal and W Symmetry; Conformal Field Theory
Issue or Number:3
Record Number:CaltechAUTHORS:20170419-081614629
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Official Citation:Simmons-Duffin, D. J. High Energ. Phys. (2017) 2017: 86. doi:10.1007/JHEP03(2017)086
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76655
Deposited By: Ruth Sustaita
Deposited On:19 Apr 2017 15:50
Last Modified:03 Oct 2019 17:03

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