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S. Ferrara and G. Parisi, Conformal covariant correlation functions
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
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
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
1973
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, Covariant expansion of the conformal four-point function
1973
Earlier work this paper cites.
A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory
1974
Earlier work this paper cites.
M.A. Olshanetsky and A.M. Perelomov, Completely integrable Hamiltonian systems connected with semisimple Lie algebras
1976
Earlier work this paper cites.
G. Mack, Duality in quantum field theory
1977
Earlier work this paper cites.
G. Mack, Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory
1977
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
1977
Earlier work this paper cites.
M.A. Olshanetsky and A.M. Perelomov, Classical integrable finite-dimensional systems related to Lie algebras
1981
Earlier work this paper cites.
M.A. Olshanetsky and A.M. Perelomov, Quantum integrable systems related to Lie algebras
1983
Earlier work this paper cites.
H. Osborn and A. C. Petkou, Implications of conformal invariance in field theories for general dimensions
1994
Earlier work this paper cites.

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2016

Harmony of Spinning Conformal Blocks

Schomerus, Volker, Sobko, Evgeny, Isachenkov, Mikhail

Understand

Conformal blocks for correlation functions of tensor operators play an increasingly important role for the conformal bootstrap programme.

We develop a universal approach to such spinning blocks through the harmonic analysis of certain bundles over a coset of the conformal group.
The resulting Casimir equations are given by a matrix version of the Calogero-Sutherland Hamiltonian that describes the scattering of interacting spinning particles in a 1-dimensional external potential.
The approach is illustrated in several examples including fermionic seed blocks in 3D CFT where they take a very simple form.

Built on

S. Ferrara and G. Parisi, Conformal covariant correlation functions
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
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
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
1973
Earlier work this paper cites.
S. Ferrara, A. F. Grillo, G. Parisi and R. Gatto, Covariant expansion of the conformal four-point function
1973
Earlier work this paper cites.
A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory
1974
Earlier work this paper cites.
M.A. Olshanetsky and A.M. Perelomov, Completely integrable Hamiltonian systems connected with semisimple Lie algebras
1976
Earlier work this paper cites.
G. Mack, Duality in quantum field theory
1977
Earlier work this paper cites.
G. Mack, Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory
1977
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
1977
Earlier work this paper cites.
M.A. Olshanetsky and A.M. Perelomov, Classical integrable finite-dimensional systems related to Lie algebras
1981
Earlier work this paper cites.
M.A. Olshanetsky and A.M. Perelomov, Quantum integrable systems related to Lie algebras
1983
Earlier work this paper cites.
H. Osborn and A. C. Petkou, Implications of conformal invariance in field theories for general dimensions
1994
Earlier work this paper cites.