Built on

P. A. M. Dirac, “Wave equations in conformal space,” Annals Math
1936
Earlier work this paper cites.
G. Mack and A. Salam, “Finite component field representations of the conformal group,” Annals Phys
1969
Earlier work this paper cites.
S. Ferrara and G. Parisi, “Conformal covariant correlation functions,” Nucl. Phys. B
1972
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, “The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products,” Lett. Nuovo Cim
1972
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and G. Parisi, “Nonequivalence between conformal covariant wilson expansion in euclidean and minkowski space,” Lett. Nuovo Cim
1972
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
1972
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
1973
Earlier work this paper cites.
S. Ferrara, R. Gatto and A. F. Grillo, “Conformal algebra in space-time and operator product expansion,” Springer Tracts Mod. Phys
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz
1974
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,” Berlin 1977, 280p
1977
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B
2001
Earlier work this paper cites.

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2016

Seed Conformal Blocks in 4D CFT

Echeverri, Alejandro Castedo, Elkhidir, Emtinan, Karateev, Denis et al.

Understand

We compute in closed analytical form the minimal set of "seed" conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (l,\bar l) of the Lorentz group in four dimensional conformal field theories.

These blocks arise from 4-point functions involving two scalars, one (0,|l-\bar l|) and one (|l-\bar l|,0) spinors or tensors.
We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any (l,\bar l), by using an educated ansatz and reducing the problem to an algebraic linear system.
Various details on the form of the ansatz have been deduced by using the so called shadow formalism.

Built on

P. A. M. Dirac, “Wave equations in conformal space,” Annals Math
1936
Earlier work this paper cites.
G. Mack and A. Salam, “Finite component field representations of the conformal group,” Annals Phys
1969
Earlier work this paper cites.
S. Ferrara and G. Parisi, “Conformal covariant correlation functions,” Nucl. Phys. B
1972
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, “The shadow operator formalism for conformal algebra. Vacuum expectation values and operator products,” Lett. Nuovo Cim
1972
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and G. Parisi, “Nonequivalence between conformal covariant wilson expansion in euclidean and minkowski space,” Lett. Nuovo Cim
1972
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
1972
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
1973
Earlier work this paper cites.
S. Ferrara, R. Gatto and A. F. Grillo, “Conformal algebra in space-time and operator product expansion,” Springer Tracts Mod. Phys
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz
1974
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,” Berlin 1977, 280p
1977
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys. B
2001
Earlier work this paper cites.