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Title: Bootstrapping 3D fermions with global symmetries

Abstract

We study the conformal bootstrap for 4-point functions of fermions < ψ i ψ j ψ k ψ ℓ > in parity-preserving 3d CFTs, where ψ i transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N . For values of N for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.

Authors:
 [1];  [2];  [3];  [1];  [4]
+ Show Author Affiliations
  1. Princeton Univ., NJ (United States). Joseph Henry Lab.
  2. Univ. of California, Berkeley, CA (United States). Berkeley Center for Theoretical Physics. Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Theoretical Physics Group
  3. Yale Univ., New Haven, CT (United States). Dept. of Physics
  4. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Institute for Advanced Study, Princeton, NJ (United States); Princeton Univ., NJ (United States); Yale Univ., New Haven, CT (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Simons Foundation (United States)
OSTI Identifier:
1494081
Grant/Contract Number:  
AC02-05CH11231; SC0009988; PHY-1418069; PHY-1350180; 488653; 488651; 488657
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: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N expansion; conformal and W symmetry; conformal field theory; global symmetries

Citation Formats

Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., and Simmons-Duffin, David. Bootstrapping 3D fermions with global symmetries. United States: N. p., 2018. Web. doi:10.1007/jhep01(2018)036.
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Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., & Simmons-Duffin, David. Bootstrapping 3D fermions with global symmetries. United States. https://doi.org/10.1007/jhep01(2018)036
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Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., and Simmons-Duffin, David. Tue . "Bootstrapping 3D fermions with global symmetries". United States. https://doi.org/10.1007/jhep01(2018)036. https://www.osti.gov/servlets/purl/1494081.
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@article{osti_1494081,
title = {Bootstrapping 3D fermions with global symmetries},
author = {Iliesiu, Luca and Kos, Filip and Poland, David and Pufu, Silviu S. and Simmons-Duffin, David},
abstractNote = {We study the conformal bootstrap for 4-point functions of fermions < ψ i ψ j ψ k ψ ℓ > in parity-preserving 3d CFTs, where ψ i transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N . For values of N for which the Gross-Neveu-Yukawa universality classes are relevant to condensed-matter systems, we compare our results to previous analytic and numerical results.},
doi = {10.1007/jhep01(2018)036},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2018,
place = {United States},
year = {2018},
month = {1}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1007/jhep01(2018)036
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Cited by: 23 works
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Figures / Tables:

Table 1 Table 1: Top: representations and one-loop dimensions of low-lying operators in the 3D GNY models. V , S, T, A denote the vector, singlet, rank-two traceless symmetric tensor, and rank-two antisymmetric tensor representations of O(N), respectively. At large N, the dimensions of ψi was computed, while the dimension of $\bar{ψ}$(iψj)more » was computed in appendix B. We list no corrections for dimension of the lowest operator in the O(N) anti-symmetric representation, as we could not find any discussion of it in the literature. The most recent ϵ-expansion estimates for the scaling dimensions are available, where O(ϵ3) corrections are available for the dimensions associated to ψi and φ. Prior work on the ϵ-expansion for the GNY models can be found in [28-33]. Bottom: representations and one-loop values for the central charges for the O(N) conserved current and for the stress-energy tensor at large N as determined in [45].« less
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    Works referencing / citing this record:

    The 3d stress-tensor bootstrap
    journal, February 2018

    • Dymarsky, Anatoly; Kos, Filip; Kravchuk, Petr
    • Journal of High Energy Physics, Vol. 2018, Issue 2
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    From spinning conformal blocks to matrix Calogero-Sutherland models
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    Solving M-theory with the conformal bootstrap
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    • Agmon, Nathan B.; Chester, Shai M.; Pufu, Silviu S.
    • Journal of High Energy Physics, Vol. 2018, Issue 6
    • DOI: 10.1007/jhep06(2018)159

    Fermion conformal bootstrap in 4d
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    • Karateev, Denis; Kravchuk, Petr; Serone, Marco
    • Journal of High Energy Physics, Vol. 2019, Issue 6
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    Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
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    • Journal of High Energy Physics, Vol. 2019, Issue 10
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    Elective-momentum ultrasize quantum Monte Carlo method
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    Momentum dependence of quantum critical Dirac systems
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    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

    The 3d Stress-Tensor Bootstrap
    text, January 2017

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

    Solving M-theory with the Conformal Bootstrap
    text, January 2017

    Scalar CFTs and Their Large N Limits
    text, January 2017

    Fermion-induced quantum criticality with two length scales in Dirac systems
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    text, January 2018

    Critical behavior of Dirac fermions from perturbative renormalization
    text, January 2018

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