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CFT unitarity and the AdS Cutkosky rules

Meltzer, David and Sivaramakrishnan, Allic (2020) CFT unitarity and the AdS Cutkosky rules. Journal of High Energy Physics, 2020 (11). Art. No. 73. ISSN 1126-6708. doi:10.1007/JHEP11(2020)073.

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We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

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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: September 3, 2020; Accepted: October 8, 2020; Published: November 16, 2020. We thank Soner Albayrak, Simon Caron-Huot, Clifford Cheung, Savan Kharel, Per Kraus, Julio Parra-Martinez, Eric Perlmutter, and David Simmons-Duffin for discussions. We also thank Julio Parra-Martinez for comments on the draft. AS thanks the Walter Burke Institute for Theoretical Physics for hospitality while this work was in progress. The research of DM is supported by Simons Foundation grant 488657, the Walter Burke Institute for Theoretical Physics and the Sherman Fairchild Foundation. AS is supported by the College of Arts and Sciences of the University of Kentucky.
Group:Walter Burke Institute for Theoretical Physics
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Simons Foundation488657
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
University of KentuckyUNSPECIFIED
Subject Keywords:1/N Expansion; AdS-CFT Correspondence; Conformal Field Theory
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Issue or Number:11
Record Number:CaltechAUTHORS:20200912-075230114
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Official Citation:Meltzer, D., Sivaramakrishnan, A. CFT unitarity and the AdS Cutkosky rules. J. High Energ. Phys. 2020, 73 (2020).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105367
Deposited By: Joy Painter
Deposited On:14 Sep 2020 17:15
Last Modified:16 Nov 2021 18:42

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