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On the four-point function of the stress-energy tensors in a CFT · Around

2013

On the four-point function of the stress-energy tensors in a CFT

Dymarsky, Anatoly

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We discuss to what extent the full set of Ward Identities constrain the four-point function of the stress-energy tensors or conserved currents in a conformal field theory.

We calculate the number of kinematically unrestricted functional degrees of freedom governing the corresponding correlators and find that it matches the number of functional degrees of freedom governing scattering amplitudes of some "dual" massless particles in the auxiliary Minkowski space.
We also formulate the conformal bootstrap constraints for the correlators in question in terms of only unrestricted degrees of freedom.
As a by-product we find interesting parallels between solving Ward Identities in coordinate and momentum space.

Built on

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A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, “Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory,” Nucl. Phys. B 241
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H. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys. 231
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P. Di Francesco, P. Mathieu and D. Senechal, “Conformal field theory,” New York, USA: Springer (1997) 890 p
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Then

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Later among the works it cites.
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Later among the works it cites.
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Later among the works it cites.
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H. Osborn, “Implications of conformal invariance for quantum field theories in d ¿ 2,” hep-th/9312176

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A. Bzowski, P. McFadden and K. Skenderis, “Implications of conformal invariance in momentum space,” arXiv:1304.7760 [hep-th]

Cited in the paper.