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Report number	arXiv:1705.01357 ; CERN-PH-TH-2017-098 ; CERN-TH-2017-098
Title	Cut-touching linear functionals in the conformal bootstrap
Related title	Cut-touching linear functionals in the conformal bootstrap
Author(s)	Qiao, Jiaxin (Ecole Normale Superieure ; UPMC, Paris (main) ; CERN) ; Rychkov, Slava (Ecole Normale Superieure ; UPMC, Paris (main) ; CERN)
Publication	2017-06-14
Imprint	2017-05-03
Number of pages	18
Note	19 pages, 7 figures, v2: author order corrected, v3: full domain of 4pt analyticity made more precise, v4: misprint corrected and acknowledgement added
In:	JHEP 06 (2017) 076
DOI	10.1007/JHEP06(2017)076
Subject category	hep-th ; Particle Physics - Theory
Abstract	The modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial "swapping" property, allowing to swap infinite summation with the action of the functional in the conformal bootstrap sum rule. Swapping is easy to justify for the popular functionals involving finite sums of derivatives. However, it is far from obvious for "cut-touching" functionals, involving integration over regions where conformal block decomposition does not converge uniformly. Functionals of this type were recently considered by Mazac in his work on analytic derivation of optimal bootstrap bounds. We derive general swapping criteria for the cut-touching functionals, and check in a few explicit examples that Mazac's functionals pass our criteria.
Copyright/License	arXiv nonexclusive-distrib. 1.0

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