Built on

S. Albayrak, D. Meltzer and D. Poland, “More Analytic Bootstrap: Nonperturbative Effects and Fermions,” JHEP 1908
Original
1904
Earlier work this paper cites.
J. F. Fortin and W. Skiba, “A recipe for conformal blocks,” arXiv:1905.00036 [hep-th]
Original
1905
Earlier work this paper cites.
W. Li, “Closed-form expression for cross-channel conformal blocks near the lightcone,” JHEP 2001
Original
1906
Earlier work this paper cites.
H. Y. Chen and H. Kyono, “On conformal blocks, crossing kernels and multi-variable hypergeometric functions,” JHEP 1910
Original
1906
Earlier work this paper cites.
S. M. Chester, “Weizmann Lectures on the Numerical Conformal Bootstrap,” arXiv:1907.05147 [hep-th]
Original
1907
Earlier work this paper cites.
R. S. Erramilli, L. V. Iliesiu and P. Kravchuk, “Recursion relation for general 3d blocks,” arXiv:1907.11247 [hep-th]
Original
1907
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 / N 2 1/N^{2} ,” arXiv:1907.02445 [hep-th]
Original
1907
Earlier work this paper cites.
I. Burić, V. Schomerus and M. Isachenkov, “Conformal Group Theory of Tensor Structures,” arXiv:1910.08099 [hep-th]
Original
1910
Earlier work this paper cites.
M. F. Paulos, “Analytic Functional Bootstrap for CFTs in d > 1 d>1 ,” arXiv:1910.08563 [hep-th]
Original
1910
Earlier work this paper cites.
D. Mazáč, L. Rastelli and X. Zhou, “A Basis of Analytic Functionals for CFTs in General Dimension,” arXiv:1910.12855 [hep-th]
Original
1910
Earlier work this paper cites.
D. Carmi and S. Caron-Huot, “A Conformal Dispersion Relation: Correlations from Absorption,” arXiv:1910.12123 [hep-th]
Original
1910
Earlier work this paper cites.
A. Bissi, P. Dey and T. Hansen, “Dispersion Relation for CFT Four-Point Functions,” arXiv:1910.04661 [hep-th]
Original
1910
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys. 76
1973
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, “Covariant expansion of the conformal four-point function,” Nucl. Phys. B 49
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz. 66
1974
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, R. Gatto and G. Parisi, “Analyticity properties and asymptotic expansions of conformal covariant green’s functions,” Nuovo Cim. A 19
1974
Earlier work this paper cites.
S. Ferrara, R. Gatto and A. F. Grillo, “Properties of Partial Wave Amplitudes in Conformal Invariant Field Theories,” Nuovo Cim. A 26
1975
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. D 13
1976
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, “Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory,” Nucl. Phys. B 241
1984
Earlier work this paper cites.
A. B. Zamolodchikov, “Conformal symmetry in two-dimensional space: Recursion representation of conformal block,” Theoretical and Mathematical Physics 73 no. 1, (1987) 1088–1093
1987
Earlier work this paper cites.
K. Lang and W. Ruhl, “The Critical O(N) sigma model at dimensions 2 < < d < < 4: Fusion coefficients and anomalous dimensions,” Nucl. Phys. B 400
1993
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B 599
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal partial waves and the operator product expansion,” Nucl. Phys. B 678
2003
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, “Comments on operators with large spin,” JHEP 0711
Original
2007
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.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, “Spinning Conformal Blocks,” JHEP 1111
Original
2011
Earlier work this paper cites.
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. D 86
Original
2012
Earlier work this paper cites.
D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, “OPE Convergence in Conformal Field Theory,” Phys. Rev. D 86
Original
2012
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.
M. Hogervorst and S. Rychkov, “Radial Coordinates for Conformal Blocks,” Phys. Rev. D 87
Original
2013
Earlier work this paper cites.
A. L. Fitzpatrick, J. Kaplan and D. Poland, “Conformal Blocks in the Large D D Limit,” JHEP 1308
Original
2013
Earlier work this paper cites.
M. Hogervorst, H. Osborn and S. Rychkov, “Diagonal Limit for Conformal Blocks in d d Dimensions,” JHEP 1308
Original
2013
Earlier work this paper cites.

Similar

A. L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, “The Analytic Bootstrap and AdS Superhorizon Locality,” JHEP 1312
Original
2013
Cited alongside, same era.
Z. Komargodski and A. Zhiboedov, “Convexity and Liberation at Large Spin,” JHEP 1311
Original
2013
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 II. c-Minimization and Precise Critical Exponents,” J. Stat. Phys. 157
Original
2014
Cited alongside, same era.
F. Kos, D. Poland and D. Simmons-Duffin, “Bootstrapping Mixed Correlators in the 3D Ising Model,” JHEP 1411
Original
2014
Cited alongside, same era.
F. Kos, D. Poland and D. Simmons-Duffin, “Bootstrapping the O ⁡ ( N ) O(N) vector models,” JHEP 1406

Then

J. Qiao and S. Rychkov, “A tauberian theorem for the conformal bootstrap,” JHEP 1712
Original
2017
Later among the works it cites.
L. F. Alday and A. Zhiboedov, “An Algebraic Approach to the Analytic Bootstrap,” JHEP 1704
Original
2017
Later among the works it cites.
L. F. Alday and A. Bissi, “Crossing symmetry and Higher spin towers,” JHEP 1712
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.
L. F. Alday, “Solving CFTs with Weakly Broken Higher Spin Symmetry,” JHEP 1710
Original

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

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2019

Lightcone expansions of conformal blocks in closed form

Li, Wenliang

Understand

We present new closed-form expressions for 4-point scalar conformal blocks in the s- and t-channel lightcone expansions.

Our formulae apply to intermediate operators of arbitrary spin in general dimensions.
For physical spin $\ell$, they are composed of at most $(\ell+1)$ Gaussian hypergeometric functions at each order.

Built on

S. Albayrak, D. Meltzer and D. Poland, “More Analytic Bootstrap: Nonperturbative Effects and Fermions,” JHEP 1908
Original
1904
Earlier work this paper cites.
J. F. Fortin and W. Skiba, “A recipe for conformal blocks,” arXiv:1905.00036 [hep-th]
Original
1905
Earlier work this paper cites.
W. Li, “Closed-form expression for cross-channel conformal blocks near the lightcone,” JHEP 2001
Original
1906
Earlier work this paper cites.
H. Y. Chen and H. Kyono, “On conformal blocks, crossing kernels and multi-variable hypergeometric functions,” JHEP 1910
Original
1906
Earlier work this paper cites.
S. M. Chester, “Weizmann Lectures on the Numerical Conformal Bootstrap,” arXiv:1907.05147 [hep-th]
Original
1907
Earlier work this paper cites.
R. S. Erramilli, L. V. Iliesiu and P. Kravchuk, “Recursion relation for general 3d blocks,” arXiv:1907.11247 [hep-th]
Original
1907
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 / N 2 1/N^{2} ,” arXiv:1907.02445 [hep-th]
Original
1907
Earlier work this paper cites.
I. Burić, V. Schomerus and M. Isachenkov, “Conformal Group Theory of Tensor Structures,” arXiv:1910.08099 [hep-th]
Original
1910
Earlier work this paper cites.
M. F. Paulos, “Analytic Functional Bootstrap for CFTs in d > 1 d>1 ,” arXiv:1910.08563 [hep-th]
Original
1910
Earlier work this paper cites.
D. Mazáč, L. Rastelli and X. Zhou, “A Basis of Analytic Functionals for CFTs in General Dimension,” arXiv:1910.12855 [hep-th]
Original
1910
Earlier work this paper cites.
D. Carmi and S. Caron-Huot, “A Conformal Dispersion Relation: Correlations from Absorption,” arXiv:1910.12123 [hep-th]
Original
1910
Earlier work this paper cites.
A. Bissi, P. Dey and T. Hansen, “Dispersion Relation for CFT Four-Point Functions,” arXiv:1910.04661 [hep-th]
Original
1910
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys. 76
1973
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, “Covariant expansion of the conformal four-point function,” Nucl. Phys. B 49
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz. 66
1974
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, R. Gatto and G. Parisi, “Analyticity properties and asymptotic expansions of conformal covariant green’s functions,” Nuovo Cim. A 19
1974
Earlier work this paper cites.
S. Ferrara, R. Gatto and A. F. Grillo, “Properties of Partial Wave Amplitudes in Conformal Invariant Field Theories,” Nuovo Cim. A 26
1975
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. D 13
1976
Earlier work this paper cites.
A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, “Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory,” Nucl. Phys. B 241
1984
Earlier work this paper cites.
A. B. Zamolodchikov, “Conformal symmetry in two-dimensional space: Recursion representation of conformal block,” Theoretical and Mathematical Physics 73 no. 1, (1987) 1088–1093
1987
Earlier work this paper cites.
K. Lang and W. Ruhl, “The Critical O(N) sigma model at dimensions 2 < < d < < 4: Fusion coefficients and anomalous dimensions,” Nucl. Phys. B 400
1993
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B 599
2001
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal partial waves and the operator product expansion,” Nucl. Phys. B 678
2003
Earlier work this paper cites.
L. F. Alday and J. M. Maldacena, “Comments on operators with large spin,” JHEP 0711
Original
2007
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.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, “Spinning Conformal Blocks,” JHEP 1111
Original
2011
Earlier work this paper cites.
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. D 86
Original
2012
Earlier work this paper cites.
D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, “OPE Convergence in Conformal Field Theory,” Phys. Rev. D 86
Original
2012
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.
M. Hogervorst and S. Rychkov, “Radial Coordinates for Conformal Blocks,” Phys. Rev. D 87
Original
2013
Earlier work this paper cites.
A. L. Fitzpatrick, J. Kaplan and D. Poland, “Conformal Blocks in the Large D D Limit,” JHEP 1308
Original
2013
Earlier work this paper cites.
M. Hogervorst, H. Osborn and S. Rychkov, “Diagonal Limit for Conformal Blocks in d d Dimensions,” JHEP 1308
Original
2013
Earlier work this paper cites.

Similar

A. L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, “The Analytic Bootstrap and AdS Superhorizon Locality,” JHEP 1312
Original
2013
Cited alongside, same era.
Z. Komargodski and A. Zhiboedov, “Convexity and Liberation at Large Spin,” JHEP 1311
Original
2013
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 II. c-Minimization and Precise Critical Exponents,” J. Stat. Phys. 157
Original
2014
Cited alongside, same era.
F. Kos, D. Poland and D. Simmons-Duffin, “Bootstrapping Mixed Correlators in the 3D Ising Model,” JHEP 1411
Original
2014
Cited alongside, same era.
F. Kos, D. Poland and D. Simmons-Duffin, “Bootstrapping the O ⁡ ( N ) O(N) vector models,” JHEP 1406

Then

J. Qiao and S. Rychkov, “A tauberian theorem for the conformal bootstrap,” JHEP 1712
Original
2017
Later among the works it cites.
L. F. Alday and A. Zhiboedov, “An Algebraic Approach to the Analytic Bootstrap,” JHEP 1704
Original
2017
Later among the works it cites.
L. F. Alday and A. Bissi, “Crossing symmetry and Higher spin towers,” JHEP 1712
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.
L. F. Alday, “Solving CFTs with Weakly Broken Higher Spin Symmetry,” JHEP 1710
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…

Original

2014

Cited alongside, same era.

D. Simmons-Duffin, “Projectors, Shadows, and Conformal Blocks,” JHEP 1404

Original

2014

Cited alongside, same era.

M. S. Costa and T. Hansen, “Conformal correlators of mixed-symmetry tensors,” JHEP 1502

Original

2015

Cited alongside, same era.

A. Castedo Echeverri, E. Elkhidir, D. Karateev and M. Serone, “Deconstructing Conformal Blocks in 4D CFT,” JHEP 1508

Original

2015

Cited alongside, same era.

G. Vos, “Generalized Additivity in Unitary Conformal Field Theories,” Nucl. Phys. B 899

Original

2015

Cited alongside, same era.

A. Kaviraj, K. Sen and A. Sinha, “Analytic bootstrap at large spin,” JHEP 1511

Original

2015

Cited alongside, same era.

L. F. Alday, A. Bissi and T. Lukowski, “Large spin systematics in CFT,” JHEP 1511

Original

2015

Cited alongside, same era.

A. Kaviraj, K. Sen and A. Sinha, “Universal anomalous dimensions at large spin and large twist,” JHEP 1507

Original

2015

Cited alongside, same era.

2017