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Tailoring three-point functions and integrability

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Abstract

We use integrability techniques to compute structure constants in \( \mathcal{N} = 4 \) SYM to leading order at weak coupling and to leading order in the planar expansion. Three closed spin chains, which represent the single trace gauge-invariant operators in \( \mathcal{N} = 4 \) SYM, are cut into six open chains which are then sewed back together into some nice pants, the three-point function. The algebraic and coordinate Bethe ansatz tools necessary for this task are reviewed. Our results hold for scalar single trace operators of arbitrary size. Finally, we discuss the classical limit of our results, anticipating some predictions for quasi-classical string correlators in terms of algebraic curves.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario, N2L 2Y5, Canada

    Jorge Escobedo, Amit Sever & Pedro Vieira

  2. Department of Physics and Astronomy & Guelph-Waterloo Physics Institute, University of Waterloo, 200 University Av. W., Waterloo, Ontario, N2L 3G1, Canada

    Jorge Escobedo

  3. Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, U.K.

    Nikolay Gromov

  4. St. Petersburg INP, Gatchina, 188300, St. Petersburg, Russia

    Nikolay Gromov

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  1. Jorge Escobedo
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Correspondence to Jorge Escobedo.

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ArXiv ePrint: 1012.2475

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Escobedo, J., Gromov, N., Sever, A. et al. Tailoring three-point functions and integrability. J. High Energ. Phys. 2011, 28 (2011). https://doi.org/10.1007/JHEP09(2011)028

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