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002262551 001__ 2262551
002262551 005__ 20231004080158.0
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002262551 0247_ $$2DOI$$9bibmatch$$a10.1007/JHEP06(2017)076
002262551 037__ $$9arXiv$$aarXiv:1705.01357$$chep-th
002262551 035__ $$9arXiv$$aoai:arXiv.org:1705.01357
002262551 037__ $$aCERN-PH-TH-2017-098
002262551 035__ $$9Inspire$$aoai:inspirehep.net:1598062$$d2023-10-03T08:06:19Z$$h2023-10-04T02:18:14Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002262551 037__ $$aCERN-TH-2017-098
002262551 035__ $$9Inspire$$a1598062
002262551 041__ $$aeng
002262551 100__ $$aQiao, Jiaxin$$uCERN$$uUPMC, Paris (main)$$uEcole Normale Superieure$$vLaboratoire de Physique Théorique - Département de Physique de l’ENS - École Normale Supérieure - PSL Research U. - Sorbonne Universités - UPMC Univ. Paris 06 - CNRS - 75005 - Paris - France$$vCERN - Theoretical Physics Department - 1211 - Geneva 23 - Switzerland
002262551 245__ $$9arXiv$$aCut-touching linear functionals in the conformal bootstrap
002262551 246__ $$9arXiv$$aCut-touching linear functionals in the conformal bootstrap
002262551 269__ $$c2017-05-03
002262551 260__ $$c2017-06-14
002262551 300__ $$a18 p
002262551 500__ $$9arXiv$$a19 pages, 7 figures, v2: author order corrected, v3: full domain of 4pt analyticity made more precise, v4: misprint corrected and acknowledgement added
002262551 520__ $$9Springer$$aThe modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial “swapping” property, allowing to swap infinite summation with the action of the functional in the conformal bootstrap sum rule. Swapping is easy to justify for the popular functionals involving finite sums of derivatives. However, it is far from obvious for “cut-touching” functionals, involving integration over regions where conformal block decomposition does not converge uniformly. Functionals of this type were recently considered by Mazáč in his work on analytic derivation of optimal bootstrap bounds. We derive general swapping criteria for the cut-touching functionals, and check in a few explicit examples that Mazáč’s functionals pass our criteria.
002262551 520__ $$9arXiv$$aThe modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial "swapping" property, allowing to swap infinite summation with the action of the functional in the conformal bootstrap sum rule. Swapping is easy to justify for the popular functionals involving finite sums of derivatives. However, it is far from obvious for "cut-touching" functionals, involving integration over regions where conformal block decomposition does not converge uniformly. Functionals of this type were recently considered by Mazac in his work on analytic derivation of optimal bootstrap bounds. We derive general swapping criteria for the cut-touching functionals, and check in a few explicit examples that Mazac's functionals pass our criteria.
002262551 540__ $$aarXiv nonexclusive-distrib. 1.0$$barXiv$$uhttp://arxiv.org/licenses/nonexclusive-distrib/1.0/
002262551 595__ $$aProcessed with process_update_harvested_ph_th_arxiv_native_record function
002262551 595__ $$aCERN-TH
002262551 65017 $$2arXiv$$ahep-th
002262551 65017 $$2SzGeCERN$$aParticle Physics - Theory
002262551 690C_ $$aCERN
002262551 700__ $$aRychkov, Slava$$uCERN$$uUPMC, Paris (main)$$uEcole Normale Superieure$$vLaboratoire de Physique Théorique - Département de Physique de l’ENS - École Normale Supérieure - PSL Research U. - Sorbonne Universités - UPMC Univ. Paris 06 - CNRS - 75005 - Paris - France$$vCERN - Theoretical Physics Department - 1211 - Geneva 23 - Switzerland
002262551 773__ $$c076$$pJHEP$$v06$$y2017
002262551 8564_ $$81310768$$s856300$$uhttp://cds.cern.ch/record/2262551/files/arXiv:1705.01357.pdf
002262551 8564_ $$81310761$$s51155$$uhttp://cds.cern.ch/record/2262551/files/contMazac.png$$y00005 The contour used in the definition of basis functionals \reef{basis}.
002262551 8564_ $$81310762$$s40373$$uhttp://cds.cern.ch/record/2262551/files/Gammaz.png$$y00003 Contour $\Gamma_z$\,. Also shown are the two cuts of the cut plane.
002262551 8564_ $$81310763$$s43245$$uhttp://cds.cern.ch/record/2262551/files/Gammax.png$$y00004 Contour $\Gamma_x$\,. Also shown are the images of the two cuts of the cut plane under the transformation from $z$ to $x$. The function $h(x)$ and the functions $f(z(x))$ on which the functional is evaluated will be analytic in the upper half-plane.
002262551 8564_ $$81310764$$s42542$$uhttp://cds.cern.ch/record/2262551/files/regF.png$$y00001 A region of uniform convergence of the series in the crossing relation \reef{cross}.
002262551 8564_ $$81310765$$s68364$$uhttp://cds.cern.ch/record/2262551/files/S.png$$y00002 Support of integration in the functional of Example 1.
002262551 8564_ $$81310766$$s66314$$uhttp://cds.cern.ch/record/2262551/files/contMazacMod.png$$y00006 The contours used in \reef{hsplit-cont}. It is important that $\Gamma_1$ goes around $x=0$, while $\Gamma_2$ passes through it.
002262551 8564_ $$81310767$$s28709$$uhttp://cds.cern.ch/record/2262551/files/regG.png$$y00000 A region where the series \reef{CBexp} converges uniformly (the image of the disk $|\rho|\le 1-\eps$ in the $z$ plane).
002262551 8564_ $$81332600$$s644665$$uhttp://cds.cern.ch/record/2262551/files/scoap3-fulltext.pdf$$yArticle from SCOAP3
002262551 8564_ $$82333446$$s644665$$uhttp://cds.cern.ch/record/2262551/files/scoap.pdf$$yArticle from SCOAP3
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002262551 980__ $$aArticle
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