An algebraic approach to the analytic bootstrap

Alday, Luis F.; Zhiboedov, Alexander

doi:10.1007/JHEP04(2017)157

Title: An algebraic approach to the analytic bootstrap

Journal Article · Thu Apr 27 00:00:00 EDT 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP04(2017)157· OSTI ID:1368372

Alday, Luis F. ^[1]; Zhiboedov, Alexander ^[2]

Univ. of Oxford (United Kingdom). Mathematical Inst.
Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature

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. Here, 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.

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Research Organization:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); European Research Council (ERC)

Grant/Contract Number:: SC0007870; 306260

OSTI ID:: 1368372

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 4; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 95 works

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