Meltzer, David
(2021)
*Dispersion Formulas in QFTs, CFTs, and Holography.*
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(Unpublished)
https://resolver.caltech.edu/CaltechAUTHORS:20210408-121857560

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## Abstract

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

Item Type: | Report or Paper (Discussion Paper) | ||||||||
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Additional Information: | We thank Adam Bzowski, Simon Caron-Huot, Marc Gillioz, Savan Kharel, Sebastian Mizera, Julio Parra-Martinez, Eric Perlmutter, David Simmons-Duffin, Allic Sivaramakrishnan, Kostas Skenderis, Edward Witten, and Roman Zwicky for discussions. We would also thank Savan Kharel, Julio Parra-Martinez, and Allic Sivaramakrishnan for comments on the draft. The research of DM is supported by the Walter Burke Institute for Theoretical Physics and the Sherman Fairchild Foundation. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. | ||||||||

Group: | Walter Burke Institute for Theoretical Physics | ||||||||

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Record Number: | CaltechAUTHORS:20210408-121857560 | ||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210408-121857560 | ||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||

ID Code: | 108658 | ||||||||

Collection: | CaltechAUTHORS | ||||||||

Deposited By: | Tony Diaz | ||||||||

Deposited On: | 09 Apr 2021 17:58 | ||||||||

Last Modified: | 09 Apr 2021 17:58 |

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