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V. N. Gribov, Possible Asymptotic Behavior of Elastic Scattering , JETP Lett. 41
1961
Earlier work this paper cites.
G. Mack, Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory , Commun. Math. Phys. 53
1977
Earlier work this paper cites.
G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N=4 SYM(4) in supergravity approximation , Phys. Rev. D62
2000
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.
T. Huber and D. Maitre, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters , Comput. Phys. Commun. 175
2006
Earlier work this paper cites.
F. A. Dolan, M. Nirschl and H. Osborn, Conjectures for large N superconformal N=4 chiral primary four point functions , Nucl. Phys. B749
2006
Earlier work this paper cites.
T. Huber and D. Maitre, HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters , Comput. Phys. Commun. 178
Original
2008
Earlier work this paper cites.
A. L. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-Matrix , JHEP 10
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 12
Original
2013
Earlier work this paper cites.

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2019

Bissi, Agnese, Dey, Parijat, Hansen, Tobias

We present a dispersion relation in conformal field theory which expresses the four point function as an integral over its single discontinuity.

Exploiting the analytic properties of the OPE and crossing symmetry of the correlator, we show that in perturbative settings the correlator depends only on the spectrum of the theory, as well as the OPE coefficients of certain low twist operators, and can be reconstructed unambiguously.
In contrast to the Lorentzian inversion formula, the validity of the dispersion relation does not assume Regge behavior and is not restricted to the exchange of spinning operators.
As an application, the correlator $\langle \phi \phi \phi \phi \rangle$ in $\phi^4$ theory at the Wilson-Fisher fixed point is computed in closed form to order $\epsilon^2$ in the $\epsilon$ expansion.

V. N. Gribov, Possible Asymptotic Behavior of Elastic Scattering , JETP Lett. 41
1961
Earlier work this paper cites.
G. Mack, Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory , Commun. Math. Phys. 53
1977
Earlier work this paper cites.
G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N=4 SYM(4) in supergravity approximation , Phys. Rev. D62
2000
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.
T. Huber and D. Maitre, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters , Comput. Phys. Commun. 175
2006
Earlier work this paper cites.
F. A. Dolan, M. Nirschl and H. Osborn, Conjectures for large N superconformal N=4 chiral primary four point functions , Nucl. Phys. B749
2006
Earlier work this paper cites.
T. Huber and D. Maitre, HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters , Comput. Phys. Commun. 178
Original
2008
Earlier work this paper cites.
A. L. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-Matrix , JHEP 10
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 12
Original
2013
Earlier work this paper cites.