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A. Z. Patashinskii and V. L. Pokrovskii, “Second Order Phase Transitions in a Bose Fluid,” JETP
1964
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi, and R. Gatto, “The shadow operator formalism for conformal algebra. vacuum expectation values and operator products,” Lettere al Nuovo Cimento (1971-1985)
1972
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum heisenberg magnet,” Phys. Rev. Lett
1993
Earlier work this paper cites.
H. Liu, “Scattering in anti-de Sitter space and operator product expansion,” Phys. Rev
1999
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys
2001
Earlier work this paper cites.
A. Karch and L. Randall, “Locally localized gravity,” JHEP
2001
Earlier work this paper cites.
I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully, “Holography from Conformal Field Theory,” JHEP
Original
2009
Earlier work this paper cites.
R. Gurau, “Colored Group Field Theory,” Commun. Math. Phys
Original
2011
Earlier work this paper cites.
V. Bonzom, R. Gurau, A. Riello, and V. Rivasseau, “Critical behavior of colored tensor models in the large N limit,” Nucl. Phys
Original
2011
Earlier work this paper cites.
J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP
Original
2011
Earlier work this paper cites.

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2017

Gross, David J., Rosenhaus, Vladimir

Large $N$ melonic theories are characterized by two-point function Feynman diagrams built exclusively out of melons.

This leads to conformal invariance at strong coupling, four-point function diagrams that are exclusively ladders, and higher-point functions that are built out of four-point functions joined together.
We uncover an incredibly useful property of these theories: the six-point function, or equivalently, the three-point function of the primary $O(N)$ invariant bilinears, regarded as an analytic function of the operator dimensions, fully determines all correlation functions, to leading nontrivial order in $1/N$, through simple Feynman-like rules.
The result is applicable to any theory, not necessarily melonic, in which higher-point correlators are built out of four-point functions.

A. Z. Patashinskii and V. L. Pokrovskii, “Second Order Phase Transitions in a Bose Fluid,” JETP
1964
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi, and R. Gatto, “The shadow operator formalism for conformal algebra. vacuum expectation values and operator products,” Lettere al Nuovo Cimento (1971-1985)
1972
Earlier work this paper cites.
S. Sachdev and J. Ye, “Gapless spin-fluid ground state in a random quantum heisenberg magnet,” Phys. Rev. Lett
1993
Earlier work this paper cites.
H. Liu, “Scattering in anti-de Sitter space and operator product expansion,” Phys. Rev
1999
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys
2001
Earlier work this paper cites.
A. Karch and L. Randall, “Locally localized gravity,” JHEP
2001
Earlier work this paper cites.
I. Heemskerk, J. Penedones, J. Polchinski, and J. Sully, “Holography from Conformal Field Theory,” JHEP
Original
2009
Earlier work this paper cites.
R. Gurau, “Colored Group Field Theory,” Commun. Math. Phys
Original
2011
Earlier work this paper cites.
V. Bonzom, R. Gurau, A. Riello, and V. Rivasseau, “Critical behavior of colored tensor models in the large N limit,” Nucl. Phys
Original
2011
Earlier work this paper cites.
J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP
Original
2011
Earlier work this paper cites.