Built on

H. Osborn, “Conformal Blocks for Arbitrary Spins in Two Dimensions,” Phys. Lett
Original
1941
Earlier work this paper cites.
M. D’Eramo, G. Parisi, and L. Peliti, “Theoretical Predictions For Critical Exponents at the lambda point of Boise Liquids,” Lett. Nuovo Cim
1971
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
1977
Earlier work this paper cites.
G. Passarino and M. J. G. Veltman, “One Loop Corrections for e+ e- Annihilation Into mu+ mu- in the Weinberg Model,” Nucl. Phys
1979
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. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys
1994
Earlier work this paper cites.
A. Bialas, H. Navelet, and R. B. Peschanski, “High mass diffraction in the QCD dipole picture,” Phys. Lett
1998
Earlier work this paper cites.
G. P. Korchemsky, “Conformal bootstrap for the BFKL pomeron,” Nucl. Phys
1999
Earlier work this paper cites.
D. Z. Freedman, S. D. Mathur, A. Matusis, and L. Rastelli, “Correlation functions in the CFT(d) / AdS(d+1) correspondence,” Nucl. Phys
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.
B. Ponsot and J. Teschner, “Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U(q)(sl(2,R)),” Commun. Math. Phys
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal partial waves and the operator product expansion,” Nucl. Phys
2004
Earlier work this paper cites.
B. Ponsot, “Recent progresses on Liouville field theory,” Int. J. Mod. Phys
2004
Earlier work this paper cites.
J. Murakami and M. Yano, “On the volume of a hyperbolic and spherical tetrahedron,” Communications in Analysis and Geometry
2005
Earlier work this paper cites.
K. Krasnov and J. Louko, “SO(1,d+1) Racah coefficients: Type I representations,” J. Math. Phys
2006
Earlier work this paper cites.
R. S. Ismagilov, “Racah operators for principal series of representations of the group SL ( 2 , ℂ ) \text{SL}(2,\mathbb{C}) ,” Sbornik: Mathematics
2007
Earlier work this paper cites.
L. Cornalba, M. S. Costa, J. Penedones, and R. Schiappa, “Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions,” Nucl. Phys
2007
Earlier work this paper cites.
T. Hartman and L. Rastelli, “Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT,” JHEP
2008
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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2018

$d$-dimensional SYK, AdS Loops, and $6j$ Symbols

Liu, Junyu, Perlmutter, Eric, Rosenhaus, Vladimir et al.

Understand

We study the $6j$ symbol for the conformal group, and its appearance in three seemingly unrelated contexts: the SYK model, conformal representation theory, and perturbative amplitudes in AdS.

The contribution of the planar Feynman diagrams to the three-point function of the bilinear singlets in SYK is shown to be a $6j$ symbol.
We generalize the computation of these and other Feynman diagrams to $d$ dimensions.
The $6j$ symbol can be viewed as the crossing kernel for conformal partial waves, which may be computed using the Lorentzian inversion formula.

Built on

H. Osborn, “Conformal Blocks for Arbitrary Spins in Two Dimensions,” Phys. Lett
Original
1941
Earlier work this paper cites.
M. D’Eramo, G. Parisi, and L. Peliti, “Theoretical Predictions For Critical Exponents at the lambda point of Boise Liquids,” Lett. Nuovo Cim
1971
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
1977
Earlier work this paper cites.
G. Passarino and M. J. G. Veltman, “One Loop Corrections for e+ e- Annihilation Into mu+ mu- in the Weinberg Model,” Nucl. Phys
1979
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. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys
1994
Earlier work this paper cites.
A. Bialas, H. Navelet, and R. B. Peschanski, “High mass diffraction in the QCD dipole picture,” Phys. Lett
1998
Earlier work this paper cites.
G. P. Korchemsky, “Conformal bootstrap for the BFKL pomeron,” Nucl. Phys
1999
Earlier work this paper cites.
D. Z. Freedman, S. D. Mathur, A. Matusis, and L. Rastelli, “Correlation functions in the CFT(d) / AdS(d+1) correspondence,” Nucl. Phys
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.
B. Ponsot and J. Teschner, “Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U(q)(sl(2,R)),” Commun. Math. Phys
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal partial waves and the operator product expansion,” Nucl. Phys
2004
Earlier work this paper cites.
B. Ponsot, “Recent progresses on Liouville field theory,” Int. J. Mod. Phys
2004
Earlier work this paper cites.
J. Murakami and M. Yano, “On the volume of a hyperbolic and spherical tetrahedron,” Communications in Analysis and Geometry
2005
Earlier work this paper cites.
K. Krasnov and J. Louko, “SO(1,d+1) Racah coefficients: Type I representations,” J. Math. Phys
2006
Earlier work this paper cites.
R. S. Ismagilov, “Racah operators for principal series of representations of the group SL ( 2 , ℂ ) \text{SL}(2,\mathbb{C}) ,” Sbornik: Mathematics
2007
Earlier work this paper cites.
L. Cornalba, M. S. Costa, J. Penedones, and R. Schiappa, “Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions,” Nucl. Phys
2007
Earlier work this paper cites.
T. Hartman and L. Rastelli, “Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT,” JHEP
2008
Earlier work this paper cites.
J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP
Original
2011
Earlier work this paper cites.