Built on

G. Mack and A. Salam, Finite component field representations of the conformal group , Ann. Phys. 53
1969
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion , Annals Phys. 76
1973
Earlier work this paper cites.
A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory , Zh. Eksp. Teor. Fiz. 66
1974
Earlier work this paper cites.
W. E. Caswell, Asymptotic Behavior of Nonabelian Gauge Theories to Two Loop Order , Phys. Rev. Lett. 33
1974
Earlier work this paper cites.
V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova and I. T. Todorov, Harmonic Analysis on the n-Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory , Lect. Notes Phys. 63
1977
Earlier work this paper cites.
G. Mack, All Unitary Ray Representations of the Conformal Group S U ( 2 , 2 ) SU(2,2) with Positive Energy , Commun.Math.Phys. 55
1977
Earlier work this paper cites.
T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions , Nucl. Phys. B196
1982
Earlier work this paper cites.
Al. B. Zamolodchikov, Conformal symmetry in two-dimensional space: Recursion representation of conformal block , Theoretical and Mathematical Physics 73
1987
Earlier work this paper cites.
Princeton University Press, Princeton, NJ, USA, 1992
J. Wess and J. Bagger, Supersymmetry and supergravity · 1992
Earlier work this paper cites.
H. Osborn and A. C. Petkou, Implications of conformal invariance in field theories for general dimensions , Annals Phys. 231
1994
Earlier work this paper cites.
F. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl.Phys. B599
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B599
2001
Earlier work this paper cites.
F. Dolan and H. Osborn, Conformal partial waves and the operator product expansion , Nucl.Phys. B678
2004
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion , Nucl. Phys. B678
2004
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 12
Original
2008
Earlier work this paper cites.
V. S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
F. Caracciolo and V. S. Rychkov, Rigorous Limits on the Interaction Strength in Quantum Field Theory , Phys. Rev. D81
Original
2010
Earlier work this paper cites.
R. Rattazzi, S. Rychkov and A. Vichi, Central Charge Bounds in 4D Conformal Field Theory , Phys. Rev. D83
Original
2011
Earlier work this paper cites.
R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4D Conformal Field Theories with Global Symmetry , J. Phys. A44
Original
2011
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Correlators , JHEP 1111
Original
2011
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Blocks , JHEP 1111
Original
2011
Earlier work this paper cites.
S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap , Phys.Rev. D86
Original
2012
Earlier work this paper cites.

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Then

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Original
2016
Later among the works it cites.
Y. Nakayama and T. Ohtsuki, Necessary Condition for Emergent Symmetry from the Conformal Bootstrap , Phys. Rev. Lett. 117
Original
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Later among the works it cites.
T. DeGrand, Lattice tests of beyond Standard Model dynamics , Rev. Mod. Phys. 88
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2016
Later among the works it cites.
F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Precision Islands in the Ising and O ⁡ ( N ) O(N) Models , JHEP 08
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Later among the works it cites.
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2019

Fermion Conformal Bootstrap in 4d

Karateev, Denis, Kravchuk, Petr, Serone, Marco et al.

Understand

We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs.

We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies.
We find discontinuities in some of the bounds on operator dimensions, and we show that they arise due to a generic yet previously unobserved fake primary effect, which is related to the existence of poles in conformal blocks.
We show that this effect is also responsible for similar discontinuities found in four-fermion bootstrap in 3d, as well as in the mixed-correlator analysis of the 3d Ising CFT.

Built on

G. Mack and A. Salam, Finite component field representations of the conformal group , Ann. Phys. 53
1969
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion , Annals Phys. 76
1973
Earlier work this paper cites.
A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory , Zh. Eksp. Teor. Fiz. 66
1974
Earlier work this paper cites.
W. E. Caswell, Asymptotic Behavior of Nonabelian Gauge Theories to Two Loop Order , Phys. Rev. Lett. 33
1974
Earlier work this paper cites.
V. K. Dobrev, G. Mack, V. B. Petkova, S. G. Petrova and I. T. Todorov, Harmonic Analysis on the n-Dimensional Lorentz Group and Its Application to Conformal Quantum Field Theory , Lect. Notes Phys. 63
1977
Earlier work this paper cites.
G. Mack, All Unitary Ray Representations of the Conformal Group S U ( 2 , 2 ) SU(2,2) with Positive Energy , Commun.Math.Phys. 55
1977
Earlier work this paper cites.
T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions , Nucl. Phys. B196
1982
Earlier work this paper cites.
Al. B. Zamolodchikov, Conformal symmetry in two-dimensional space: Recursion representation of conformal block , Theoretical and Mathematical Physics 73
1987
Earlier work this paper cites.
Princeton University Press, Princeton, NJ, USA, 1992
J. Wess and J. Bagger, Supersymmetry and supergravity · 1992
Earlier work this paper cites.
H. Osborn and A. C. Petkou, Implications of conformal invariance in field theories for general dimensions , Annals Phys. 231
1994
Earlier work this paper cites.
F. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl.Phys. B599
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B599
2001
Earlier work this paper cites.
F. Dolan and H. Osborn, Conformal partial waves and the operator product expansion , Nucl.Phys. B678
2004
Earlier work this paper cites.
F. A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion , Nucl. Phys. B678
2004
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 12
Original
2008
Earlier work this paper cites.
V. S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions , Phys. Rev. D80
Original
2009
Earlier work this paper cites.
F. Caracciolo and V. S. Rychkov, Rigorous Limits on the Interaction Strength in Quantum Field Theory , Phys. Rev. D81
Original
2010
Earlier work this paper cites.
R. Rattazzi, S. Rychkov and A. Vichi, Central Charge Bounds in 4D Conformal Field Theory , Phys. Rev. D83
Original
2011
Earlier work this paper cites.
R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4D Conformal Field Theories with Global Symmetry , J. Phys. A44
Original
2011
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Correlators , JHEP 1111
Original
2011
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, Spinning Conformal Blocks , JHEP 1111
Original
2011
Earlier work this paper cites.
S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap , Phys.Rev. D86
Original
2012
Earlier work this paper cites.