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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 > 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]
  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); Inst. 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) (SC-25); 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:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
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.
Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., & Simmons-Duffin, David. Bootstrapping 3D fermions with global symmetries. United States. doi:10.1007/jhep01(2018)036.
Iliesiu, Luca, Kos, Filip, Poland, David, Pufu, Silviu S., and Simmons-Duffin, David. Tue . "Bootstrapping 3D fermions with global symmetries". United States. doi:10.1007/jhep01(2018)036. https://www.osti.gov/servlets/purl/1494081.
@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)},
issn = {1029-8479},
number = 1,
volume = 2018,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 20 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 referenced in this record:

Bootstrapping 3D fermions
journal, March 2016

  • Iliesiu, Luca; Kos, Filip; Poland, David
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)120

Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
journal, May 2014


Superconducting quantum criticality of topological surface states at three loops
journal, November 2016


Bootstrapping the O(N) archipelago
journal, November 2015

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)106

Critical exponents of new universality classes
journal, September 1993


Accidental symmetries and the conformal bootstrap
journal, January 2016

  • Chester, Shai M.; Giombi, Simone; Iliesiu, Luca V.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)110

Bootstrapping the O(N ) vector models
journal, June 2014

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)091

Convergence of derivative expansion in supersymmetric functional RG flows
journal, February 2015

  • Heilmann, Marianne; Hellwig, Tobias; Knorr, Benjamin
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)109

Precision islands in the Ising and O(N ) models
journal, August 2016

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)036

Bootstrapping O(N ) vector models with four supercharges in 3 ≤ d ≤ 4
journal, May 2016

  • Chester, Shai M.; Iliesiu, Luca V.; Pufu, Silviu S.
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)103

Bounds on 4D conformal and superconformal field theories
journal, May 2011

  • Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)017

UV completions of composite Higgs models with partial compositeness
journal, February 2013

  • Caracciolo, Francesco; Parolini, Alberto; Serone, Marco
  • Journal of High Energy Physics, Vol. 2013, Issue 2
  • DOI: 10.1007/JHEP02(2013)066

Interactions and Phase Transitions on Graphene’s Honeycomb Lattice
journal, October 2006


Topological Mott Insulator in Three-Dimensional Systems with Quadratic Band Touching
journal, September 2014


Emergent Space-Time Supersymmetry at the Boundary of a Topological Phase
journal, April 2014


Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
journal, April 2016


Quantum field theory in the large N limit: a review
journal, October 2003


The minimal composite Higgs model
journal, July 2005


Notes on spinning operators in fermionic CFT
journal, May 2017

  • Giombi, S.; Kirilin, V.; Skvortsov, E.
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)041

Anomalous mass dimension at O(1/N2) in the O(N) Gross-Neveu model
journal, December 1992


Fermionic quantum critical point of spinless fermions on a honeycomb lattice
journal, October 2014


Bootstrapping Conformal Field Theories with the Extremal Functional Method
journal, December 2013


Quantum Phase Transitions in d -Wave Superconductors
journal, December 2000


Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
journal, October 2017


Critical behaviour of the three-dimensional Gross-Neveu and Higgs-Yukawa models
journal, March 1994


COMPUTATION OF CRITICAL EXPONENT η AT O(1/N 3 ) IN THE FOUR-FERMI MODEL IN ARBITRARY DIMENSIONS
journal, February 1994


Non-Fermi-Liquid and Topological States with Strong Spin-Orbit Coupling
journal, November 2013


Duality in quantum field theory
journal, February 1977


Phase transition and critical behavior of the d =3 Gross-Neveu model
journal, November 2002


Fermionic quantum criticality in honeycomb and π -flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
journal, April 2015

  • Parisen Toldin, Francesco; Hohenadler, Martin; Assaad, Fakher F.
  • Physical Review B, Vol. 91, Issue 16
  • DOI: 10.1103/PhysRevB.91.165108

The lightcone bootstrap and the spectrum of the 3d Ising CFT
journal, March 2017


Operator product expansions and consistency relations in a O(N) invariant fermionic CFT for 2 < d < 4
journal, December 1996


A semidefinite program solver for the conformal bootstrap
journal, June 2015


Bounds on OPE coefficients in 4D Conformal Field Theories
journal, October 2014

  • Caracciolo, Francesco; Echeverri, Alejandro Castedo; von Harling, Benedict
  • Journal of High Energy Physics, Vol. 2014, Issue 10
  • DOI: 10.1007/JHEP10(2014)020

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973


Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2014, Issue 11
  • DOI: 10.1007/JHEP11(2014)109

Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents
journal, June 2014

  • El-Showk, Sheer; Paulos, Miguel F.; Poland, David
  • Journal of Statistical Physics, Vol. 157, Issue 4-5
  • DOI: 10.1007/s10955-014-1042-7

Ising and Gross-Neveu model in next-to-leading order
journal, December 2016


Bootstrapping the Three Dimensional Supersymmetric Ising Model
journal, July 2015


Quantum phase transitions
journal, November 2003


Three-loop calculations in the O(N) gross-neveu model
journal, September 1990


    Works referencing / citing this record:

    Momentum dependence of quantum critical Dirac systems
    journal, June 2019