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2022

From conformal correlators to analytic S-matrices: CFT$_1$/QFT$_2$

Córdova, Lucía, He, Yifei, Paulos, Miguel F.

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We study families of one-dimensional CFTs relevant for describing gapped QFTs in AdS$_2$.

Using the Polyakov bootstrap as our main tool, we explain how S-matrices emerge from the flat space limit of CFT correlators.
In this limit we prove that the CFT OPE density matches that of a generalized free field, and that this implies unitarity of the S-matrix.
We establish a CFT dispersion formula for the S-matrix, proving its analyticity except for singularities on the real axis which we characterize in terms of the CFT data.

From conformal correlators to analytic S-matrices: CFT$_1$/QFT$_2$ · Around

Built on

M. F. Paulos and B. Zan, “A functional approach to the numerical conformal bootstrap,”
Original
1904
Earlier work this paper cites.
A. Homrich, J. a. Penedones, J. Toledo, B. C. van Rees, and P. Vieira, “The S-matrix Bootstrap IV: Multiple Amplitudes,”
Original
1905
Earlier work this paper cites.
B. Gabai and X. Yin, “On The S-Matrix of Ising Field Theory in Two Dimensions,”
Original
1905
Earlier work this paper cites.
E. Hijano, “Flat space physics from AdS/CFT,”
Original
1905
Earlier work this paper cites.
J. Elias Miró, A. L. Guerrieri, A. Hebbar, J. a. Penedones, and P. Vieira, “Flux Tube S-matrix Bootstrap,”
Original
1906
Earlier work this paper cites.
L. Córdova, Y. He, M. Kruczenski, and P. Vieira, “The O(N) S-matrix Monolith,”
Original
1909
Earlier work this paper cites.
A. Bissi, P. Dey, and T. Hansen, “Dispersion Relation for CFT Four-Point Functions,”
Original
1910
Earlier work this paper cites.
D. Karateev, S. Kuhn, and J. a. Penedones, “Bootstrapping Massive Quantum Field Theories,”
Original
1912
Earlier work this paper cites.
D. Meltzer, E. Perlmutter, and A. Sivaramakrishnan, “Unitarity Methods in AdS/CFT,”
Original
1912
Earlier work this paper cites.
L. D. Landau, “On analytic properties of vertex parts in quantum field theory,”
1959
Earlier work this paper cites.
R. E. Cutkosky, “Singularities and discontinuities of Feynman amplitudes,”
1960
Earlier work this paper cites.
J. Bros, H. Epstein, and V. Glaser, “A proof of the crossing property for two-particle amplitudes in general quantum field theory,”
1965
Earlier work this paper cites.
A. Martin, “Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity. 1.,”
1965
Earlier work this paper cites.
Cambridge Univ. Press, Cambridge, 1966
R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, · 1966
Earlier work this paper cites.
G. Sommer, “Present state of rigorous analytic properties of scattering amplitudes,”
1970
Earlier work this paper cites.
M. Creutz, “Rigorous bounds on coupling constants in two-dimensional field theories,”
1972
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,”
1974
Earlier work this paper cites.
M. Luscher and G. Mack, “Global Conformal Invariance in Quantum Field Theory,”
1975
Earlier work this paper cites.
S. R. Coleman and H. J. Thun, “On the Prosaic Origin of the Double Poles in the Sine-Gordon S Matrix,”
1978
Earlier work this paper cites.
I. R. Klebanov and E. Witten, “AdS / CFT correspondence and symmetry breaking,”
1999
Earlier work this paper cites.
D. Z. Freedman, S. D. Mathur, A. Matusis, and L. Rastelli, “Comments on 4 point functions in the CFT / AdS correspondence,”
1999
Earlier work this paper cites.
E. D’Hoker, S. D. Mathur, A. Matusis, and L. Rastelli, “The Operator product expansion of N=4 SYM and the 4 point functions of supergravity,”
2000
Earlier work this paper cites.
P. Kravchuk, J. Qiao, and S. Rychkov, “Distributions in CFT. Part I. Cross-ratio space,”
Original
2001
Earlier work this paper cites.
M. Correia, A. Sever, and A. Zhiboedov, “An Analytical Toolkit for the S-matrix Bootstrap,”
Original
2006
Earlier work this paper cites.

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