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Title: The 3d stress-tensor bootstrap

Abstract

We study the conformal bootstrap for 4-point functions of stress tensors in parity-preserving 3d CFTs. To set up the bootstrap equations, we analyze the constraints of conformal symmetry, permutation symmetry, and conservation on the stress-tensor 4-point function and identify a non-redundant set of crossing equations. Studying these equations numerically using semidefinite optimization, we compute bounds on the central charge as a function of the independent coefficient in the stress-tensor 3-point function. With no additional assumptions, these bounds numerically reproduce the conformal collider bounds and give a general lower bound on the central charge. We also study the effect of gaps in the scalar, spin-2, and spin-4 spectra on the central charge bound. We find general upper bounds on these gaps as well as tighter restrictions on the stress-tensor 3-point function coefficients for theories with moderate gaps. When the gap for the leading scalar or spin-2 operator is sufficiently large to exclude large N theories, we also obtain upper bounds on the central charge, thus finding compact allowed regions. Finally, assuming the known low-lying spectrum and central charge of the critical 3d Ising model, we determine its stress-tensor 3-point function and derive a bound on its leading parity-odd scalar.

Authors:
 [1];  [2]; ORCiD logo [3];  [4];  [5]
+ Show Author Affiliations
  1. Univ. of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy; Skolkovo Inst. of Science and Technology, Moscow (Russian Federation). Skolkovo Innovation Center
  2. Univ. of California, Berkeley, CA (United States). Berkeley Center for Theoretical Physics and Dept. of Physics ; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group
  3. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
  4. Yale Univ., New Haven, CT (United States). Dept. of Physics
  5. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics; Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division; National Science Foundation (NSF); Simons Foundation; USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1461289
Alternate Identifier(s):
OSTI ID: 1493252; OSTI ID: 1597659
Grant/Contract Number:  
SC0009988; SC0011632; AC02-05CH11231; PHY-1720374; 488657; PHY-1350180; 488651
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: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; AdS-CFT Correspondence; Conformal and W Symmetry; Field Theories in Higher Dimensions

Citation Formats

Dymarsky, Anatoly, Kos, Filip, Kravchuk, Petr, Poland, David, and Simmons-Duffin, David. The 3d stress-tensor bootstrap. United States: N. p., 2018. Web. doi:10.1007/JHEP02(2018)164.
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Dymarsky, Anatoly, Kos, Filip, Kravchuk, Petr, Poland, David, & Simmons-Duffin, David. The 3d stress-tensor bootstrap. United States. https://doi.org/10.1007/JHEP02(2018)164
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Dymarsky, Anatoly, Kos, Filip, Kravchuk, Petr, Poland, David, and Simmons-Duffin, David. Tue . "The 3d stress-tensor bootstrap". United States. https://doi.org/10.1007/JHEP02(2018)164. https://www.osti.gov/servlets/purl/1461289.
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@article{osti_1461289,
title = {The 3d stress-tensor bootstrap},
author = {Dymarsky, Anatoly and Kos, Filip and Kravchuk, Petr and Poland, David and Simmons-Duffin, David},
abstractNote = {We study the conformal bootstrap for 4-point functions of stress tensors in parity-preserving 3d CFTs. To set up the bootstrap equations, we analyze the constraints of conformal symmetry, permutation symmetry, and conservation on the stress-tensor 4-point function and identify a non-redundant set of crossing equations. Studying these equations numerically using semidefinite optimization, we compute bounds on the central charge as a function of the independent coefficient in the stress-tensor 3-point function. With no additional assumptions, these bounds numerically reproduce the conformal collider bounds and give a general lower bound on the central charge. We also study the effect of gaps in the scalar, spin-2, and spin-4 spectra on the central charge bound. We find general upper bounds on these gaps as well as tighter restrictions on the stress-tensor 3-point function coefficients for theories with moderate gaps. When the gap for the leading scalar or spin-2 operator is sufficiently large to exclude large N theories, we also obtain upper bounds on the central charge, thus finding compact allowed regions. Finally, assuming the known low-lying spectrum and central charge of the critical 3d Ising model, we determine its stress-tensor 3-point function and derive a bound on its leading parity-odd scalar.},
doi = {10.1007/JHEP02(2018)164},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2018,
place = {United States},
year = {2018},
month = {2}
}
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https://doi.org/10.1007/JHEP02(2018)164
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text, January 1971

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text, January 2011

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text, January 2012

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text, January 2013

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text, January 2013

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text, January 2014

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text, January 2014

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text, January 2015

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text, January 2015

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text, January 2016

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text, January 2016

Precision Islands in the Ising and $O(N)$ Models
text, January 2016

Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
text, January 2016

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text, January 2017

Long-range critical exponents near the short-range crossover
text, January 2017

Bootstrapping 3D Fermions with Global Symmetries
text, January 2017

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    Works referencing / citing this record:

    Spheres, charges, instantons, and bootstrap: A five-dimensional odyssey
    journal, March 2018

    • Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan
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    Fermion conformal bootstrap in 4d
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    • Journal of High Energy Physics, Vol. 2019, Issue 6
    • DOI: 10.1007/jhep06(2019)088

    Beyond a = c : gravitational couplings to matter and the stress tensor OPE
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    Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
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    • Isachenkov, Mikhail; Schomerus, Volker
    • Journal of High Energy Physics, Vol. 2018, Issue 7
    • DOI: 10.1007/jhep07(2018)180

    Higher spin ANEC and the space of CFTs
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    • Gillioz, Marc; Lu, Xiaochuan; Luty, Markus A.
    • Journal of High Energy Physics, Vol. 2018, Issue 9
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    Scalar CFTs and their large N limits
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    Harmonic analysis and mean field theory
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    • Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
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    • DOI: 10.1007/jhep11(2018)140

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    Recursion relation for general 3d blocks
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    • Erramilli, Rajeev S.; Iliesiu, Luca V.; Kravchuk, Petr
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    • DOI: 10.1007/jhep12(2019)116

    Bootstrapping the long-range Ising model in three dimensions
    journal, January 2019

    Bounds on amplitudes in effective theories with massive spinning particles
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    The conformal bootstrap: Theory, numerical techniques, and applications
    journal, January 2019

    From spinning conformal blocks to matrix Calogero-Sutherland models
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    From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models
    text, January 2017

    Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
    text, January 2018

    Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
    text, January 2017

    Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
    text, January 2017

    Scalar CFTs and Their Large N Limits
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    Beyond $a=c$: Gravitational Couplings to Matter and the Stress Tensor OPE
    text, January 2017

    The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
    text, January 2018

    autoboot: A generator of bootstrap equations with global symmetry
    preprint, January 2019

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