An algebraic approach to the analytic bootstrap
Abstract
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 Borelsummable 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 twoloop 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.
 Authors:
 Univ. of Oxford (United Kingdom). Mathematical Inst.
 Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature
 Publication Date:
 Research Org.:
 Harvard Univ., Cambridge, MA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC); European Research Council (ERC)
 OSTI Identifier:
 1368372
 Grant/Contract Number:
 SC0007870; 306260
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 4; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal Field Theory; AdSCFT Correspondence
Citation Formats
Alday, Luis F., and Zhiboedov, Alexander. An algebraic approach to the analytic bootstrap. United States: N. p., 2017.
Web. doi:10.1007/JHEP04(2017)157.
Alday, Luis F., & Zhiboedov, Alexander. An algebraic approach to the analytic bootstrap. United States. doi:10.1007/JHEP04(2017)157.
Alday, Luis F., and Zhiboedov, Alexander. 2017.
"An algebraic approach to the analytic bootstrap". United States.
doi:10.1007/JHEP04(2017)157. https://www.osti.gov/servlets/purl/1368372.
@article{osti_1368372,
title = {An algebraic approach to the analytic bootstrap},
author = {Alday, Luis F. and Zhiboedov, Alexander},
abstractNote = {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 Borelsummable 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 twoloop 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.},
doi = {10.1007/JHEP04(2017)157},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2017,
place = {United States},
year = 2017,
month = 4
}
Web of Science

Analytic and algebraic evaluation of FranckCondon overlap integrals
The problem of calculating FranckCondon intensities in Polyatomic molecules remains of great interest. This calculation requires the knowledge of the wave functions of the initial and final states and the successive evaluation of the overlap integrals. It has been suggested that algebraic methods provide a way to obtain wave functions of polyatomic molecules. An analytic and algebraic evaluation of FranckCondon overlap integrals for harmonic oscillators displaced by an amount {Delta} and of different frequencies ({omega}, {omega}{prime}) is presented. The results are extended to Morse oscillators to first order in effective anharmonicities.