Towards Feynman rules for conformal blocks
- Creators
- Hoback, Sarah
- Parikh, Sarthak
Abstract
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.
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).Attached Files
Published - Hoback-Parikh2021_Article_TowardsFeynmanRulesForConforma.pdf
Submitted - 2006.14736.pdf
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Additional details
- Eprint ID
- 107366
- Resolver ID
- CaltechAUTHORS:20210107-131434378
- Pomona College
- Caltech
- Created
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2021-01-08Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field