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Cut-touching linear functionals in the conformal bootstrap · Around

2017

Cut-touching linear functionals in the conformal bootstrap

Qiao, Jiaxin, Rychkov, Slava

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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.

Built on

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1973
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A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,”
1974
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G. Mack, “Duality in quantum field theory,”
1977
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A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, “Infinite conformal symmetry in two-dimensional quantum field theory,”
1984
Earlier work this paper cites.
F. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,”
2001
Earlier work this paper cites.

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F. Dolan and H. Osborn, “Conformal Partial Waves: Further Mathematical Results,”
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Cited in the paper.

Then

SpringerBriefs in Physics. 2016
Original
S. Rychkov, · 2016
Later among the works it cites.
A. Castedo Echeverri, B. von Harling, and M. Serone, “The Effective Bootstrap,”
Original
2016
Later among the works it cites.
https://www.youtube.com/watch?v=Q1Tefm1FQhA . Simons Bootstrap Collaboration Online Seminar (Jan 18, 2016)
D. Mazáč · 2016
Later among the works it cites.
D. Mazáč, “Analytic Bounds and Emergence of
Original
2017
Closest in time.

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