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Towards Feynman rules for conformal blocks

Hoback, Sarah and Parikh, Sarthak (2021) Towards Feynman rules for conformal blocks. Journal of High Energy Physics, 2021 (1). Art. No. 5. ISSN 1029-8479.

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We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

Item Type:Article
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URLURL TypeDescription Paper
Parikh, Sarthak0000-0002-5831-3873
Additional Information:© 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: July 22, 2020; Revised: October 24, 2020; Accepted: November 16, 2020; Published: January 4, 2021. The work of S. H. was partially supported by the SCS Summer Research Grant, by the Pomona RAISE Grant, and by Caltech’s Visiting Undergraduate Research Program (VURP).
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Subject Keywords:Conformal Field Theory; AdS-CFT Correspondence; Conformal and W Symmetry
Issue or Number:1
Record Number:CaltechAUTHORS:20210107-131434378
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Official Citation:Hoback, S., Parikh, S. Towards Feynman rules for conformal blocks. J. High Energ. Phys. 2021, 5 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107366
Deposited By: Tony Diaz
Deposited On:08 Jan 2021 17:48
Last Modified:08 Jan 2021 17:48

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