An algebraic approach to the analytic bootstrap

A bstract We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous...

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Vydáno v:	The journal of high energy physics Ročník 2017; číslo 4; s. 1 - 37
Hlavní autoři:	Alday, Luis F., Zhiboedov, Alexander
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2017 Springer Nature B.V Springer Berlin SpringerOpen
Témata:	AdS-CFT Correspondence Algebra Channels Classical and Quantum Gravitation CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Conformal Field Theory Electric current Elementary Particles Exchange High energy physics Mathematical analysis Mathematical models MATHEMATICS AND COMPUTING Operators Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory Spintronics String Theory AdS-CFT Correspondence Conformal Field Theory
ISSN:	1029-8479, 1029-8479
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Popis
Shrnutí:	A bstract We develop an algebraic approach to the analytic bootstrap in CFTs. By acting with the Casimir operator on the crossing equation we map the problem of doing large spin sums to any desired order to the problem of solving a set of recursion relations. We compute corrections to the anomalous dimension of large spin operators due to the exchange of a primary and its descendants in the crossed channel and show that this leads to a Borel-summable expansion. We analyse higher order corrections to the microscopic CFT data in the direct channel and its matching to infinite towers of operators in the crossed channel. We apply this method to the critical O ( N ) model. At large N we reproduce the first few terms in the large spin expansion of the known two-loop anomalous dimensions of higher spin currents in the traceless symmetric representation of O ( N ) and make further predictions. At small N we present the results for the truncated large spin expansion series of anomalous dimensions of higher spin currents.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 SC0007870; 306260 USDOE Office of Science (SC) European Research Council (ERC)
ISSN:	1029-8479 1029-8479
DOI:	10.1007/JHEP04(2017)157