Built on

P. Liendo, Y. Linke and V. Schomerus, A Lorentzian inversion formula for defect CFT , 1903.05222
Original
1903
Earlier work this paper cites.
S. Albayrak, D. Meltzer and D. Poland, More Analytic Bootstrap: Nonperturbative Effects and Fermions , 1904.00032
Original
1904
Earlier work this paper cites.
W. Li, Closed-form expression for cross-channel conformal blocks near the lightcone , 1906.00707
Original
1906
Earlier work this paper cites.
L. F. Alday, J. Henriksson and M. van Loon, An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2 , 1907.02445
Original
1907
Earlier work this paper cites.
A. Bissi, P. Dey and T. Hansen, Dispersion Relation for CFT Four-Point Functions , 1910.04661
Original
1910
Earlier work this paper cites.
M. F. Paulos, Analytic Functional Bootstrap for CFTs in d > 1 d>1 , 1910.08563
Original
1910
Earlier work this paper cites.
D. Mazáˇc, L. Rastelli and X. Zhou, A Basis of Analytic Functionals for CFTs in General Dimension , 1910.12855
Original
1910
Earlier work this paper cites.
G. G.N. Watson, Notes on Generating Functions of Polynomials: (3) Polynomials of Legendre and Gegenbauer , Journal of the London Mathematical Society s1-8
1933
Earlier work this paper cites.
Interscience publishers inc., 1961
G. R. Screaton, ed., Dispersion Relations · 1961
Earlier work this paper cites.
M. Froissart , Phys. Rev. 123, 1053 (1961)
1961
Earlier work this paper cites.
V. N. Gribov , Zh. Eksp. Teor. Fiz. Sov. Phys. JETP 14, 478,1395 (1961)
1961
Earlier work this paper cites.
A. Martin, Unitarity and high-energy behavior of scattering amplitudes , Phys. Rev. 129
1963
Earlier work this paper cites.
Cambridge University Press, 1966
R. J. Eden, P. V. Landshoff, D. I. Olive and J. C. Polkinghorne, eds., The analytic S-matrix · 1966
Earlier work this paper cites.
A. Martin, Scattering Theory: Unitarity, Analyticity and Crossing , Lect. Notes Phys. 3
1969
Earlier work this paper cites.
V. K. Dobrev, V. B. Petkova, S. G. Petrova and I. T. Todorov, Dynamical Derivation of Vacuum Operator Product Expansion in Euclidean Conformal Quantum Field Theory , Phys. Rev. D13
1976
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. 63
1977
Earlier work this paper cites.
J. S. M. Rahman, M, Sums of products of ultraspherical functions , Journal of Mathematical Physics 26, 627 (1985)
1985
Earlier work this paper cites.

Similar

H. van Haeringen, A class of sums of Gegenbauer functions: Twenty-four sums in closed form , Journal of Mathematical Physics 27, 938 (1986)
1986
Cited alongside, same era.
Amsterdam, Netherlands: North-Holland, 1992
M. A. Shifman, ed., Vacuum structure and QCD sum rules · 1992
Cited alongside, same era.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits , Nucl. Phys. B425
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2000
Cited alongside, same era.
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2001
Cited alongside, same era.

Then

M. Hogervorst, Dimensional Reduction for Conformal Blocks , JHEP 09
Original
2016
Later among the works it cites.
D. Simmons-Duffin, The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT , JHEP 03
Original
2017
Later among the works it cites.
L. F. Alday and A. Zhiboedov, An Algebraic Approach to the Analytic Bootstrap , JHEP 04
Original
2017
Later among the works it cites.
L. F. Alday, Large Spin Perturbation Theory for Conformal Field Theories , Phys. Rev. Lett. 119
Original
2017
Later among the works it cites.
S. Caron-Huot, Analyticity in Spin in Conformal Theories , JHEP 09
Original

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2019

A Conformal Dispersion Relation: Correlations from Absorption

Carmi, Dean, Caron-Huot, Simon

Understand

We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory.

The correlator is expressed as an integral over its 'absorptive part', defined as a double discontinuity, times a theory-independent kernel which we compute explicitly.
The kernel is found by resumming the data obtained by the Lorentzian inversion formula.
For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios.

Built on

P. Liendo, Y. Linke and V. Schomerus, A Lorentzian inversion formula for defect CFT , 1903.05222
Original
1903
Earlier work this paper cites.
S. Albayrak, D. Meltzer and D. Poland, More Analytic Bootstrap: Nonperturbative Effects and Fermions , 1904.00032
Original
1904
Earlier work this paper cites.
W. Li, Closed-form expression for cross-channel conformal blocks near the lightcone , 1906.00707
Original
1906
Earlier work this paper cites.
L. F. Alday, J. Henriksson and M. van Loon, An alternative to diagrams for the critical O(N) model: dimensions and structure constants to order 1/N2 , 1907.02445
Original
1907
Earlier work this paper cites.
A. Bissi, P. Dey and T. Hansen, Dispersion Relation for CFT Four-Point Functions , 1910.04661
Original
1910
Earlier work this paper cites.
M. F. Paulos, Analytic Functional Bootstrap for CFTs in d > 1 d>1 , 1910.08563
Original
1910
Earlier work this paper cites.
D. Mazáˇc, L. Rastelli and X. Zhou, A Basis of Analytic Functionals for CFTs in General Dimension , 1910.12855
Original
1910
Earlier work this paper cites.
G. G.N. Watson, Notes on Generating Functions of Polynomials: (3) Polynomials of Legendre and Gegenbauer , Journal of the London Mathematical Society s1-8
1933
Earlier work this paper cites.
Interscience publishers inc., 1961
G. R. Screaton, ed., Dispersion Relations · 1961
Earlier work this paper cites.
M. Froissart , Phys. Rev. 123, 1053 (1961)
1961
Earlier work this paper cites.
V. N. Gribov , Zh. Eksp. Teor. Fiz. Sov. Phys. JETP 14, 478,1395 (1961)
1961
Earlier work this paper cites.
A. Martin, Unitarity and high-energy behavior of scattering amplitudes , Phys. Rev. 129
1963
Earlier work this paper cites.
Cambridge University Press, 1966
R. J. Eden, P. V. Landshoff, D. I. Olive and J. C. Polkinghorne, eds., The analytic S-matrix · 1966
Earlier work this paper cites.
A. Martin, Scattering Theory: Unitarity, Analyticity and Crossing , Lect. Notes Phys. 3
1969
Earlier work this paper cites.
V. K. Dobrev, V. B. Petkova, S. G. Petrova and I. T. Todorov, Dynamical Derivation of Vacuum Operator Product Expansion in Euclidean Conformal Quantum Field Theory , Phys. Rev. D13
1976
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. 63
1977
Earlier work this paper cites.
J. S. M. Rahman, M, Sums of products of ultraspherical functions , Journal of Mathematical Physics 26, 627 (1985)
1985
Earlier work this paper cites.

Similar

H. van Haeringen, A class of sums of Gegenbauer functions: Twenty-four sums in closed form , Journal of Mathematical Physics 27, 938 (1986)
1986
Cited alongside, same era.
Amsterdam, Netherlands: North-Holland, 1992
M. A. Shifman, ed., Vacuum structure and QCD sum rules · 1992
Cited alongside, same era.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits , Nucl. Phys. B425
1994
Cited alongside, same era.
G. Arutyunov and S. Frolov, Four point functions of lowest weight CPOs in N=4 SYM(4) in supergravity approximation , Phys. Rev. D62
2000
Cited alongside, same era.
F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion , Nucl. Phys. B599
2001
Cited alongside, same era.

Then

M. Hogervorst, Dimensional Reduction for Conformal Blocks , JHEP 09
Original
2016
Later among the works it cites.
D. Simmons-Duffin, The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT , JHEP 03
Original
2017
Later among the works it cites.
L. F. Alday and A. Zhiboedov, An Algebraic Approach to the Analytic Bootstrap , JHEP 04
Original
2017
Later among the works it cites.
L. F. Alday, Large Spin Perturbation Theory for Conformal Field Theories , Phys. Rev. Lett. 119
Original
2017
Later among the works it cites.
S. Caron-Huot, Analyticity in Spin in Conformal Theories , JHEP 09
Original

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills , Nucl. Phys. B725

2005

Cited alongside, same era.

R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory , Phys. Rev. Lett. 94

2005

Cited alongside, same era.

A. Baranov, On Series Containing Products of Legendre Polynomials, Mathematical Notes, vol. 80, no. 2, 2006. Translated from Matematicheskie Zametki, vol. 80, no. 2, 2006 ,

2006

Cited alongside, same era.

R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 12

Original

2008

Cited alongside, same era.

Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four Dimensions , JHEP 12

Original

2011

Cited alongside, same era.

S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap , Phys. Rev. D86

Original