Built on

O. Nachtmann, “Positivity constraints for anomalous dimensions,” Nucl. 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.
V. K. Dobrev, V. B. Petkova, S. G. Petrova, and I. T. Todorov, “Dynamical Derivation of Vacuum Operator Product Expansion in Euclidean Conformal Quantum Field Theory,” Phys. Rev
1976
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite conformal symmetry in two-dimensional quantum field theory,” Nucl. Phys
1984
Earlier work this paper cites.
J. A. Gracey, “Anomalous mass dimension at O(1/N**2) in the O(N) Gross-Neveu model,” Phys. Lett
1992
Earlier work this paper cites.
H. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys
1994
Earlier work this paper cites.
J. A. Gracey, “Computation of critical exponent eta at O(1/N**3) in the four Fermi model in arbitrary dimensions,” Int. J. Mod. Phys
1994
Earlier work this paper cites.
A. C. Petkou, “C(T) and C(J) up to next-to-leading order in 1/N in the conformally invariant O(N) vector model for 2 < d < 4 2<d<4 ,” Phys. Lett
1995
Earlier work this paper cites.
A. Petkou, “Conserved currents, consistency relations and operator product expansions in the conformally invariant O(N) vector model,” Annals Phys
1996
Earlier work this paper cites.
V. Borokhov, A. Kapustin, and X.-k. Wu, “Topological disorder operators in three-dimensional conformal field theory,” JHEP
2002
Earlier work this paper cites.
P. Calabrese, A. Pelissetto, and E. Vicari, “Multicritical phenomena in O(n(1)) + O(n(2)) symmetric theories,” Phys. Rev
2003
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
Earlier work this paper cites.
D. M. Hofman and J. Maldacena, “Conformal collider physics: Energy and charge correlations,” JHEP
Original
2008
Earlier work this paper cites.
V. S. Rychkov and A. Vichi, “Universal Constraints on Conformal Operator Dimensions,” Phys. Rev
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
Original
2010
Earlier work this paper cites.
A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha, and M. Smolkin, “Holographic GB gravity in arbitrary dimensions,” JHEP
Original
2010
Earlier work this paper cites.
R. Rattazzi, S. Rychkov, and A. Vichi, “Central Charge Bounds in 4D Conformal Field Theory,” Phys. Rev
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
Original
2011
Earlier work this paper cites.
R. C. Myers, S. Sachdev, and A. Singh, “Holographic Quantum Critical Transport without Self-Duality,” Phys. Rev
Original
2011
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, “Spinning Conformal Correlators,” JHEP
Original
2011
Earlier work this paper cites.

Similar

D. Poland, D. Simmons-Duffin, and A. Vichi, “Carving Out the Space of 4D CFTs,” JHEP
Original
2012
Cited alongside, same era.
A. Vichi, “Improved bounds for CFT’s with global symmetries,” JHEP
Original
2012
Cited alongside, same era.
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
Original
2012
Cited alongside, same era.
C. Beem, L. Rastelli, and B. C. van Rees, “The 𝒩 = 4 \mathcal{N}=4 Superconformal Bootstrap,” Phys.Rev.Lett
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2013
Cited alongside, same era.
D. Chowdhury, S. Raju, S. Sachdev, A. Singh, and P. Strack, “Multipoint correlators of conformal field theories: implications for quantum critical transport,” Phys. Rev

Then

A. Castedo Echeverri, E. Elkhidir, D. Karateev, and M. Serone, “Deconstructing Conformal Blocks in 4D CFT,” JHEP
Original
2015
Later among the works it cites.
D. Simmons-Duffin, “A Semidefinite Program Solver for the Conformal Bootstrap,” JHEP
Original
2015
Later among the works it cites.
L. Iliesiu, F. Kos, D. Poland, S. S. Pufu, D. Simmons-Duffin, and R. Yacoby, “Bootstrapping 3D Fermions,” JHEP
Original
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 ) models,” JHEP
Original
2016
Later among the works it cites.
M. Lemos and P. Liendo, “Bootstrapping 𝒩 = 2 \mathcal{N}=2 chiral correlators,” JHEP

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2017

Charting the space of 3D CFTs with a continuous global symmetry

Dymarsky, Anatoly, Penedones, Joao, Trevisani, Emilio et al.

Understand

We study correlation functions of a conserved spin-1 current $J_\mu$ in three dimensional Conformal Field Theories (CFTs).

We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point functions $\langle J_\mu J_\nu \mathcal O_{\Delta,\ell}\rangle $ and the four point function $\langle J_\mu J_\nu J_\rho J_\sigma \rangle $ and identify the minimal set of independent crossing symmetry conditions.
We obtain a recurrence relation for conformal blocks for generic spin-1 operators in three dimensions.
In the process, we improve several technical points, facilitating the use of recurrence relations.

Built on

O. Nachtmann, “Positivity constraints for anomalous dimensions,” Nucl. 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.
V. K. Dobrev, V. B. Petkova, S. G. Petrova, and I. T. Todorov, “Dynamical Derivation of Vacuum Operator Product Expansion in Euclidean Conformal Quantum Field Theory,” Phys. Rev
1976
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite conformal symmetry in two-dimensional quantum field theory,” Nucl. Phys
1984
Earlier work this paper cites.
J. A. Gracey, “Anomalous mass dimension at O(1/N**2) in the O(N) Gross-Neveu model,” Phys. Lett
1992
Earlier work this paper cites.
H. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys
1994
Earlier work this paper cites.
J. A. Gracey, “Computation of critical exponent eta at O(1/N**3) in the four Fermi model in arbitrary dimensions,” Int. J. Mod. Phys
1994
Earlier work this paper cites.
A. C. Petkou, “C(T) and C(J) up to next-to-leading order in 1/N in the conformally invariant O(N) vector model for 2 < d < 4 2<d<4 ,” Phys. Lett
1995
Earlier work this paper cites.
A. Petkou, “Conserved currents, consistency relations and operator product expansions in the conformally invariant O(N) vector model,” Annals Phys
1996
Earlier work this paper cites.
V. Borokhov, A. Kapustin, and X.-k. Wu, “Topological disorder operators in three-dimensional conformal field theory,” JHEP
2002
Earlier work this paper cites.
P. Calabrese, A. Pelissetto, and E. Vicari, “Multicritical phenomena in O(n(1)) + O(n(2)) symmetric theories,” Phys. Rev
2003
Earlier work this paper cites.
R. Rattazzi, V. S. Rychkov, E. Tonni, and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
Earlier work this paper cites.
D. M. Hofman and J. Maldacena, “Conformal collider physics: Energy and charge correlations,” JHEP
Original
2008
Earlier work this paper cites.
V. S. Rychkov and A. Vichi, “Universal Constraints on Conformal Operator Dimensions,” Phys. Rev
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
Original
2010
Earlier work this paper cites.
A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha, and M. Smolkin, “Holographic GB gravity in arbitrary dimensions,” JHEP
Original
2010
Earlier work this paper cites.
R. Rattazzi, S. Rychkov, and A. Vichi, “Central Charge Bounds in 4D Conformal Field Theory,” Phys. Rev
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
Original
2011
Earlier work this paper cites.
R. C. Myers, S. Sachdev, and A. Singh, “Holographic Quantum Critical Transport without Self-Duality,” Phys. Rev
Original
2011
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland, and S. Rychkov, “Spinning Conformal Correlators,” JHEP
Original
2011
Earlier work this paper cites.