Built on

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1974
Earlier work this paper cites.
H. M. Srivastava and P. G. Todorov, “An explicit formula for the generalized Bernoulli polynomials,” Journal of Mathematical Analysis and Applications, 1988, Volume 130, Issue 2, 509-513
1988
Earlier work this paper cites.
J. A. Wilson, “Asymptotics for the F 3 4 {}_{4}F_{3} Polynomials,” Journal of Approximation Theory 66
1991
Earlier work this paper cites.
G. E. Andrews, R. Askey and R Roy, “Special functions,” Cambridge University Press, 1999
1999
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. A. Dolan and H. Osborn, “Conformal partial waves and 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 0812
Original
2008
Earlier work this paper cites.
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, “Holography from Conformal Field Theory,” JHEP 0910
Original
2009
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J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP 1103
Original
2011
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A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B. C. van Rees, “A Natural Language for AdS/CFT Correlators,” JHEP 1111
Original
2011
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M. F. Paulos, “Towards Feynman rules for Mellin amplitudes,” JHEP 1110
Original
2011
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M. S. Costa, V. Goncalves and J. Penedones, “Conformal Regge theory,” JHEP 1212
Original
2012
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A. L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, “The Analytic Bootstrap and AdS Superhorizon Locality,” JHEP 1312
Original
2013
Earlier work this paper cites.

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2017

Simplifying large spin bootstrap in Mellin space

Dey, Parijat, Ghosh, Kausik, Sinha, Aninda

Understand

We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators.

By decomposing the equations in terms of continuous Hahn polynomials, we derive explicit expressions as an asymptotic expansion in inverse conformal spin to any order, reproducing the contribution of any primary operator and its descendants in the crossed channel.
The expressions are in terms of known mathematical functions and involve generalized Bernoulli (Norlund) polynomials and the Mack polynomials and enable us to derive certain universal properties.
Comparing with the recently introduced reformulated equations in terms of crossing symmetric tree level exchange Witten diagrams, we show that to leading order in anomalous dimension but to all orders in inverse conformal spin, the equations are the same as in the conventional formulation.

Built on

A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz. 66
1974
Earlier work this paper cites.
H. M. Srivastava and P. G. Todorov, “An explicit formula for the generalized Bernoulli polynomials,” Journal of Mathematical Analysis and Applications, 1988, Volume 130, Issue 2, 509-513
1988
Earlier work this paper cites.
J. A. Wilson, “Asymptotics for the F 3 4 {}_{4}F_{3} Polynomials,” Journal of Approximation Theory 66
1991
Earlier work this paper cites.
G. E. Andrews, R. Askey and R Roy, “Special functions,” Cambridge University Press, 1999
1999
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. A. Dolan and H. Osborn, “Conformal partial waves and 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 0812
Original
2008
Earlier work this paper cites.
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, “Holography from Conformal Field Theory,” JHEP 0910
Original
2009
Earlier work this paper cites.
J. Penedones, “Writing CFT correlation functions as AdS scattering amplitudes,” JHEP 1103
Original
2011
Earlier work this paper cites.
A. L. Fitzpatrick, J. Kaplan, J. Penedones, S. Raju and B. C. van Rees, “A Natural Language for AdS/CFT Correlators,” JHEP 1111
Original
2011
Earlier work this paper cites.
M. F. Paulos, “Towards Feynman rules for Mellin amplitudes,” JHEP 1110
Original
2011
Earlier work this paper cites.
M. S. Costa, V. Goncalves and J. Penedones, “Conformal Regge theory,” JHEP 1212
Original
2012
Earlier work this paper cites.
A. L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, “The Analytic Bootstrap and AdS Superhorizon Locality,” JHEP 1312
Original
2013
Earlier work this paper cites.