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Similar

D. Carmi, J. Penedones, J. A. Silva, and A. Zhiboedov, “Applications of dispersive sum rules: ϵ \epsilon -expansion and holography,” [arXiv:2009.13506 [hep-th]]
Original
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Then

R. Gopakumar, A. Kaviraj, K. Sen and A. Sinha, “Conformal Bootstrap in Mellin Space,” Phys. Rev. Lett. 118
Original
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P. Dey, A. Kaviraj and A. Sinha, “Mellin space bootstrap for global symmetry,” JHEP 07
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R. Gopakumar and A. Sinha, “On the Polyakov-Mellin bootstrap,” JHEP 12
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2021

Crossing Symmetric Dispersion Relations for Mellin Amplitudes

Gopakumar, Rajesh, Sinha, Aninda, Zahed, Ahmadullah

Understand

We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories (CFTs).

This allows us to set up the non-perturbative Polyakov bootstrap for CFTs in Mellin space on a firm foundation, thereby fixing the contact term ambiguities in the crossing symmetric blocks.
Our new approach employs certain "locality" constraints replacing the requirement of crossing symmetry in the usual fixed-$t$ dispersion relation.
Using these constraints we show that the sum rules based on the two channel dispersion relations and the present dispersion relations are identical.