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:
-
- Princeton Univ., NJ (United States). Joseph Henry Lab.
- 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
- Yale Univ., New Haven, CT (United States). Dept. of Physics
- 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.
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)},
number = 1,
volume = 2018,
place = {United States},
year = {2018},
month = {1}
}
Web of Science
Figures / Tables:

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
Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach
journal, May 2014
- Janssen, Lukas; Herbut, Igor F.
- Physical Review B, Vol. 89, Issue 20
Superconducting quantum criticality of topological surface states at three loops
journal, November 2016
- Zerf, Nikolai; Lin, Chien-Hung; Maciejko, Joseph
- Physical Review B, Vol. 94, Issue 20
Bootstrapping the O(N) archipelago
journal, November 2015
- Kos, Filip; Poland, David; Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2015, Issue 11
Critical exponents of new universality classes
journal, September 1993
- Rosenstein, B.; Kovner, A.
- Physics Letters B, Vol. 314, Issue 3-4
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
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
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
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
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
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
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
Interactions and Phase Transitions on Graphene’s Honeycomb Lattice
journal, October 2006
- Herbut, Igor F.
- Physical Review Letters, Vol. 97, Issue 14
Topological Mott Insulator in Three-Dimensional Systems with Quadratic Band Touching
journal, September 2014
- Herbut, Igor F.; Janssen, Lukas
- Physical Review Letters, Vol. 113, Issue 10
Emergent Space-Time Supersymmetry at the Boundary of a Topological Phase
journal, April 2014
- Grover, T.; Sheng, D. N.; Vishwanath, A.
- Science, Vol. 344, Issue 6181
Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
journal, April 2016
- Hesselmann, S.; Wessel, S.
- Physical Review B, Vol. 93, Issue 15
Quantum field theory in the large N limit: a review
journal, October 2003
- Moshe, Moshe; Zinn-Justin, Jean
- Physics Reports, Vol. 385, Issue 3-6
The minimal composite Higgs model
journal, July 2005
- Agashe, Kaustubh; Contino, Roberto; Pomarol, Alex
- Nuclear Physics B, Vol. 719, Issue 1-2
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
Anomalous mass dimension at O(1/N2) in the O(N) Gross-Neveu model
journal, December 1992
- Gracey, J. A.
- Physics Letters B, Vol. 297, Issue 3-4
Fermionic quantum critical point of spinless fermions on a honeycomb lattice
journal, October 2014
- Wang, Lei; Corboz, Philippe; Troyer, Matthias
- New Journal of Physics, Vol. 16, Issue 10
Bootstrapping Conformal Field Theories with the Extremal Functional Method
journal, December 2013
- El-Showk, Sheer; Paulos, Miguel F.
- Physical Review Letters, Vol. 111, Issue 24
Quantum Phase Transitions in -Wave Superconductors
journal, December 2000
- Vojta, Matthias; Zhang, Ying; Sachdev, Subir
- Physical Review Letters, Vol. 85, Issue 23
Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
journal, October 2017
- Mihaila, Luminita N.; Zerf, Nikolai; Ihrig, Bernhard
- Physical Review B, Vol. 96, Issue 16
Critical behaviour of the three-dimensional Gross-Neveu and Higgs-Yukawa models
journal, March 1994
- Kärkkäinen, L.; Lacaze, R.; Lacock, P.
- Nuclear Physics B, Vol. 415, Issue 3
COMPUTATION OF CRITICAL EXPONENT η AT O(1/N 3 ) IN THE FOUR-FERMI MODEL IN ARBITRARY DIMENSIONS
journal, February 1994
- Gracey, J. A.
- International Journal of Modern Physics A, Vol. 09, Issue 05
Non-Fermi-Liquid and Topological States with Strong Spin-Orbit Coupling
journal, November 2013
- Moon, Eun-Gook; Xu, Cenke; Kim, Yong Baek
- Physical Review Letters, Vol. 111, Issue 20
Duality in quantum field theory
journal, February 1977
- Mack, G.
- Nuclear Physics B, Vol. 118, Issue 5
Phase transition and critical behavior of the d =3 Gross-Neveu model
journal, November 2002
- Höfling, F.; Nowak, C.; Wetterich, C.
- Physical Review B, Vol. 66, Issue 20
Fermionic quantum criticality in honeycomb and -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
The lightcone bootstrap and the spectrum of the 3d Ising CFT
journal, March 2017
- Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2017, Issue 3
Operator product expansions and consistency relations in a O(N) invariant fermionic CFT for 2 < d < 4
journal, December 1996
- Petkou, Anastasios C.
- Physics Letters B, Vol. 389, Issue 1
A semidefinite program solver for the conformal bootstrap
journal, June 2015
- Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2015, Issue 6
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
Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973
- Ferrara, S.; Grillo, A. F.; Gatto, R.
- Annals of Physics, Vol. 76, Issue 1
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
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
Ising and Gross-Neveu model in next-to-leading order
journal, December 2016
- Knorr, Benjamin
- Physical Review B, Vol. 94, Issue 24
Bootstrapping the Three Dimensional Supersymmetric Ising Model
journal, July 2015
- Bobev, Nikolay; El-Showk, Sheer; Mazáč, Dalimil
- Physical Review Letters, Vol. 115, Issue 5
Quantum phase transitions
journal, November 2003
- Vojta, Matthias
- Reports on Progress in Physics, Vol. 66, Issue 12
Three-loop calculations in the O(N) gross-neveu model
journal, September 1990
- Gracey, J. A.
- Nuclear Physics B, Vol. 341, Issue 2
Works referencing / citing this record:
Momentum dependence of quantum critical Dirac systems
journal, June 2019
- Dabelow, Lennart; Gies, Holger; Knorr, Benjamin
- Physical Review D, Vol. 99, Issue 12
Solving M-theory with the conformal bootstrap
journal, June 2018
- Agmon, Nathan B.; Chester, Shai M.; Pufu, Silviu S.
- Journal of High Energy Physics, Vol. 2018, Issue 6
Solving M-theory with the conformal bootstrap
journal, June 2018
- Agmon, Nathan B.; Chester, Shai M.; Pufu, Silviu S.
- Journal of High Energy Physics, Vol. 2018, Issue 6
Momentum dependence of quantum critical Dirac systems
text, January 2019
- Dabelow, Lennart; Gies, Holger; Knorr, Benjamin
- GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt
The 3d stress-tensor bootstrap
journal, February 2018
- Dymarsky, Anatoly; Kos, Filip; Kravchuk, Petr
- Journal of High Energy Physics, Vol. 2018, Issue 2
From spinning conformal blocks to matrix Calogero-Sutherland models
journal, April 2018
- Schomerus, Volker; Sobko, Evgeny
- Journal of High Energy Physics, Vol. 2018, Issue 4
Fermion conformal bootstrap in 4d
journal, June 2019
- Karateev, Denis; Kravchuk, Petr; Serone, Marco
- Journal of High Energy Physics, Vol. 2019, Issue 6
Integrability of conformal blocks. Part I. Calogero-Sutherland scattering theory
journal, July 2018
- Isachenkov, Mikhail; Schomerus, Volker
- Journal of High Energy Physics, Vol. 2018, Issue 7
Scalar CFTs and their large N limits
journal, September 2018
- Rong, Junchen; Su, Ning
- Journal of High Energy Physics, Vol. 2018, Issue 9
Harmonic analysis and mean field theory
journal, October 2019
- Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
- Journal of High Energy Physics, Vol. 2019, Issue 10
Bootstrapping the minimal 3D SCFT
journal, November 2018
- Atanasov, Alexander; Hillman, Aaron; Poland, David
- Journal of High Energy Physics, Vol. 2018, Issue 11
Recursion relation for general 3d blocks
journal, December 2019
- Erramilli, Rajeev S.; Iliesiu, Luca V.; Kravchuk, Petr
- Journal of High Energy Physics, Vol. 2019, Issue 12
Designer Monte Carlo simulation for the Gross-Neveu-Yukawa transition
journal, February 2020
- Liu, Yuzhi; Wang, Wei; Sun, Kai
- Physical Review B, Vol. 101, Issue 6
Critical chiral Heisenberg model with the functional renormalization group
journal, February 2018
- Knorr, Benjamin
- Physical Review B, Vol. 97, Issue 7
Fermion-induced quantum criticality with two length scales in Dirac systems
journal, March 2018
- Torres, Emilio; Classen, Laura; Herbut, Igor F.
- Physical Review B, Vol. 97, Issue 12
Critical behavior of Dirac fermions from perturbative renormalization
journal, September 2018
- Ihrig, Bernhard; Mihaila, Luminita N.; Scherer, Michael M.
- Physical Review B, Vol. 98, Issue 12
Quantum critical behavior of two-dimensional Fermi systems with quadratic band touching
journal, December 2018
- Ray, Shouryya; Vojta, Matthias; Janssen, Lukas
- Physical Review B, Vol. 98, Issue 24
Elective-momentum ultrasize quantum Monte Carlo method
journal, February 2019
- Liu, Zi Hong; Xu, Xiao Yan; Qi, Yang
- Physical Review B, Vol. 99, Issue 8
The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019
- Poland, David; Rychkov, Slava; Vichi, Alessandro
- Reviews of Modern Physics, Vol. 91, Issue 1