Built on

F. Rosso, “Global aspects of conformal symmetry and the ANEC in dS and AdS,” JHEP 03
Original
1912
Earlier work this paper cites.
S. Kundu, “Renormalization Group Flows, the a a -Theorem and Conformal Bootstrap,” arXiv:1912.09479 [hep-th]
Original
1912
Earlier work this paper cites.
R. Haag, Local quantum physics: Fields, particles, algebras
1964
Earlier work this paper cites.
W. Zimmermann, “Lectures on Elementary Particles and Quantum Field Theory,” Brandeis Summer Institute in Theoretical Physics. MIT Press, Cambridge, Mass., 1970
1970
Earlier work this paper cites.
K. G. Wilson, “Renormalization group and critical phenomena. 1. Renormalization group and the Kadanoff scaling picture,” Phys. Rev. B 4
1971
Earlier work this paper cites.
K. G. Wilson, “Renormalization group and critical phenomena. 2. Phase space cell analysis of critical behavior,” Phys. Rev. B 4
1971
Earlier work this paper cites.
O. Nachtmann, “Positivity constraints for anomalous dimensions,” Nucl. Phys. B 63
1973
Earlier work this paper cites.
K. Osterwalder and R. Schrader, “Axioms For Euclidean Green’s Functions,” Commun. Math. Phys. 31
1973
Earlier work this paper cites.
K. Osterwalder and R. Schrader, “Axioms for Euclidean Green’s Functions. 2.,” Commun. Math. Phys. 42
1975
Earlier work this paper cites.
G. Mack, “Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory,” Commun. Math. Phys. 53
1977
Earlier work this paper cites.
P. Kravchuk, J. Qiao and S. Rychkov, “Distributions in CFT I. Cross-Ratio Space,” arXiv:2001.08778 [hep-th]
Original
2001
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.

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2020

A Generalized Nachtmann Theorem in CFT

Kundu, Sandipan

Understand

Correlators of unitary quantum field theories in Lorentzian signature obey certain analyticity and positivity properties.

For interacting unitary CFTs in more than two dimensions, we show that these properties impose general constraints on families of minimal twist operators that appear in the OPEs of primary operators.
In particular, we rederive and extend the convexity theorem which states that for the family of minimal twist operators with even spins appearing in the reflection-symmetric OPE of any scalar primary, twist must be a monotonically increasing convex function of the spin.
Our argument is completely non-perturbative and it also applies to the OPE of nonidentical scalar primaries in unitary CFTs, constraining the twist of spinning operators appearing in the OPE.

Built on

F. Rosso, “Global aspects of conformal symmetry and the ANEC in dS and AdS,” JHEP 03
Original
1912
Earlier work this paper cites.
S. Kundu, “Renormalization Group Flows, the a a -Theorem and Conformal Bootstrap,” arXiv:1912.09479 [hep-th]
Original
1912
Earlier work this paper cites.
R. Haag, Local quantum physics: Fields, particles, algebras
1964
Earlier work this paper cites.
W. Zimmermann, “Lectures on Elementary Particles and Quantum Field Theory,” Brandeis Summer Institute in Theoretical Physics. MIT Press, Cambridge, Mass., 1970
1970
Earlier work this paper cites.
K. G. Wilson, “Renormalization group and critical phenomena. 1. Renormalization group and the Kadanoff scaling picture,” Phys. Rev. B 4
1971
Earlier work this paper cites.
K. G. Wilson, “Renormalization group and critical phenomena. 2. Phase space cell analysis of critical behavior,” Phys. Rev. B 4
1971
Earlier work this paper cites.
O. Nachtmann, “Positivity constraints for anomalous dimensions,” Nucl. Phys. B 63
1973
Earlier work this paper cites.
K. Osterwalder and R. Schrader, “Axioms For Euclidean Green’s Functions,” Commun. Math. Phys. 31
1973
Earlier work this paper cites.
K. Osterwalder and R. Schrader, “Axioms for Euclidean Green’s Functions. 2.,” Commun. Math. Phys. 42
1975
Earlier work this paper cites.
G. Mack, “Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory,” Commun. Math. Phys. 53
1977
Earlier work this paper cites.
P. Kravchuk, J. Qiao and S. Rychkov, “Distributions in CFT I. Cross-Ratio Space,” arXiv:2001.08778 [hep-th]
Original
2001
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.