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

Abstract

In this paper. 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,R) 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 $$\{\Delta_\sigma,\Delta_\epsilon,f_{\sigma\sigma\epsilon},f_{\epsilon\epsilon\epsilon},c_T\}$$. 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.

Authors:
 [1]
+ Show Author Affiliations
  1. Inst. for Advanced Study, Princeton, NJ (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1597784
Grant/Contract Number:  
SC0009988
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Simmons-Duffin, David. The lightcone bootstrap and the spectrum of the 3d Ising CFT. United States: N. p., 2017. Web. doi:10.1007/JHEP03(2017)086.
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Simmons-Duffin, David. The lightcone bootstrap and the spectrum of the 3d Ising CFT. United States. https://doi.org/10.1007/JHEP03(2017)086
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Simmons-Duffin, David. Wed . "The lightcone bootstrap and the spectrum of the 3d Ising CFT". United States. https://doi.org/10.1007/JHEP03(2017)086. https://www.osti.gov/servlets/purl/1597784.
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@article{osti_1597784,
title = {The lightcone bootstrap and the spectrum of the 3d Ising CFT},
author = {Simmons-Duffin, David},
abstractNote = {In this paper. 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,R) 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 $\{\Delta_\sigma,\Delta_\epsilon,f_{\sigma\sigma\epsilon},f_{\epsilon\epsilon\epsilon},c_T\}$. 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.},
doi = {10.1007/JHEP03(2017)086},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2017,
place = {United States},
year = {Wed Mar 15 00:00:00 EDT 2017},
month = {Wed Mar 15 00:00:00 EDT 2017}
}
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https://doi.org/10.1007/JHEP03(2017)086
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Bootstrapping Mixed Correlators in the 3D Ising Model
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