Built on

S. Ferrara, A. F. Grillo, and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz
1974
Earlier work this paper cites.
D. J. Gross and A. Neveu, “Dynamical Symmetry Breaking in Asymptotically Free Field Theories,” Phys. Rev
1974
Earlier work this paper cites.
G. Mack, “Duality in Quantum Field Theory,” Nucl.Phys
1977
Earlier work this paper cites.
J. A. Gracey, “Three loop calculations in the O(N) Gross-Neveu model,” Nucl. Phys
1990
Earlier work this paper cites.
J. A. Gracey, “Anomalous mass dimension at O ⁡ ( 1 / N 2 ) O(1/N^{2}) in the O ⁡ ( N ) O(N) Gross-Neveu model,” Phys. Lett
1992
Earlier work this paper cites.
B. Rosenstein, H.-L. Yu, and A. Kovner, “Critical exponents of new universality classes,” Phys. Lett
1993
Earlier work this paper cites.
J. A. Gracey, “Computation of critical exponent eta at O ⁡ ( 1 / N 3 ) O(1/N^{3}) in the four Fermi model in arbitrary dimensions,” Int. J. Mod. Phys
1994
Earlier work this paper cites.
L. Kärkkäinen, R. Lacaze, P. Lacock, and B. Petersson, “Critical behaviour of the three-dimensional gross-neveu and higgs-yukawa models,” Nucl. Phys
1995
Earlier work this paper cites.
A. C. Petkou, “Operator product expansions and consistency relations in a O ⁡ ( N ) O(N) invariant fermionic CFT for 2 < d < 4 2<d<4 ,” Phys.Lett
1996
Earlier work this paper cites.
M. Vojta, Y. Zhang, and S. Sachdev, “Quantum Phase Transitions in d-Wave Superconductors,” Phys. Rev. Lett
2000
Earlier work this paper cites.
F. Hofling, C. Nowak, and C. Wetterich, “Phase transition and critical behavior of the D = 3 Gross-Neveu model,” Phys. Rev
2002
Earlier work this paper cites.
M. Moshe and J. Zinn-Justin, “Quantum field theory in the large N N limit: A Review,” Phys.Rept
2003
Earlier work this paper cites.
K. Agashe, R. Contino, and A. Pomarol, “The Minimal composite Higgs model,” Nucl. Phys
2005
Earlier work this paper cites.
I. F. Herbut, “Interactions and phase transitions on graphene’s honeycomb lattice,” Phys. Rev. Lett
2006
Earlier work this paper cites.
I. F. Herbut, V. Juricic, and O. Vafek, “Relativistic Mott criticality in graphene,” Phys. Rev
Original
2009
Earlier work this paper cites.

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2017

Bootstrapping 3D Fermions with Global Symmetries

Iliesiu, Luca, Kos, Filip, Poland, David et al.

Understand

We study the conformal bootstrap for 4-point functions of fermions $\langle \psi_i \psi_j \psi_k \psi_{\ell} \rangle$ in parity-preserving 3d CFTs, where $\psi_i$ 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.

Built on

S. Ferrara, A. F. Grillo, and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz
1974
Earlier work this paper cites.
D. J. Gross and A. Neveu, “Dynamical Symmetry Breaking in Asymptotically Free Field Theories,” Phys. Rev
1974
Earlier work this paper cites.
G. Mack, “Duality in Quantum Field Theory,” Nucl.Phys
1977
Earlier work this paper cites.
J. A. Gracey, “Three loop calculations in the O(N) Gross-Neveu model,” Nucl. Phys
1990
Earlier work this paper cites.
J. A. Gracey, “Anomalous mass dimension at O ⁡ ( 1 / N 2 ) O(1/N^{2}) in the O ⁡ ( N ) O(N) Gross-Neveu model,” Phys. Lett
1992
Earlier work this paper cites.
B. Rosenstein, H.-L. Yu, and A. Kovner, “Critical exponents of new universality classes,” Phys. Lett
1993
Earlier work this paper cites.
J. A. Gracey, “Computation of critical exponent eta at O ⁡ ( 1 / N 3 ) O(1/N^{3}) in the four Fermi model in arbitrary dimensions,” Int. J. Mod. Phys
1994
Earlier work this paper cites.
L. Kärkkäinen, R. Lacaze, P. Lacock, and B. Petersson, “Critical behaviour of the three-dimensional gross-neveu and higgs-yukawa models,” Nucl. Phys
1995
Earlier work this paper cites.
A. C. Petkou, “Operator product expansions and consistency relations in a O ⁡ ( N ) O(N) invariant fermionic CFT for 2 < d < 4 2<d<4 ,” Phys.Lett
1996
Earlier work this paper cites.
M. Vojta, Y. Zhang, and S. Sachdev, “Quantum Phase Transitions in d-Wave Superconductors,” Phys. Rev. Lett
2000
Earlier work this paper cites.
F. Hofling, C. Nowak, and C. Wetterich, “Phase transition and critical behavior of the D = 3 Gross-Neveu model,” Phys. Rev
2002
Earlier work this paper cites.
M. Moshe and J. Zinn-Justin, “Quantum field theory in the large N N limit: A Review,” Phys.Rept
2003
Earlier work this paper cites.
K. Agashe, R. Contino, and A. Pomarol, “The Minimal composite Higgs model,” Nucl. Phys
2005
Earlier work this paper cites.
I. F. Herbut, “Interactions and phase transitions on graphene’s honeycomb lattice,” Phys. Rev. Lett
2006
Earlier work this paper cites.
I. F. Herbut, V. Juricic, and O. Vafek, “Relativistic Mott criticality in graphene,” Phys. Rev
Original
2009
Earlier work this paper cites.