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  • Letter
  • Open Access

Structure constants in N=4 supersymmetric Yang-Mills theory and separation of variables

Carlos Bercini

Alexandre Homrich

Pedro Vieira

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Phys. Rev. D 110, L121901 – Published 2 December, 2024

DOI: https://doi.org/10.1103/PhysRevD.110.L121901

Abstract

We propose a new framework for computing three-point functions in planar N=4 super Yang-Mills theory where these correlators take the form of multiple integrals of separation of variables type. We test this formalism at weak coupling at leading and next-to-leading orders in a noncompact SL(2) sector of the theory and all the way to next-to-next-to-leading orders for a compact SU(2) sector. We find evidence that wrapping effects can also be incorporated.

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References (41)

  1. B. Basso, S. Komatsu, and P. Vieira, Structure constants and integrable bootstrap in planar N=4 SYM theory, arXiv:1505.06745.
  2. N. Gromov, V. Kazakov, S. Leurent, and D. Volin, Quantum spectral curve for planar N=4 super-Yang-Mills theory, Phys. Rev. Lett. 112, 011602 (2014); Quantum spectral curve for arbitrary state/operator in AdS5/CFT4, J. High Energy Phys. 09 (2015) 187.
  3. B. Basso, V. Goncalves, S. Komatsu, and P. Vieira, Gluing hexagons at three loops, Nucl. Phys. B907, 695 (2016).
  4. B. Basso, V. Goncalves, and S. Komatsu, Structure constants at wrapping order, J. High Energy Phys. 05 (2017) 124.
  5. B. Eden and A. Sfondrini, Three-point functions in N=4 SYM: The hexagon proposal at three loops, J. High Energy Phys. 02 (2016) 165.
  6. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.110.L121901 for notation used in this Letter and extra details on the derivation of the main results.
  7. R. Roiban and A. Volovich, Yang-Mills correlation functions from integrable spin chains, J. High Energy Phys. 09 (2004) 032.
  8. P. Vieira and T. Wang, Tailoring non-compact spin chains, J. High Energy Phys. 10 (2014) 035.
  9. J. Escobedo, N. Gromov, A. Sever, and P. Vieira, Tailoring three-point functions and integrability, J. High Energy Phys. 09 (2011) 028.
  10. S. E. Derkachov, G. P. Korchemsky, and A. N. Manashov, Separation of variables for the quantum SL(2,R) spin chain, J. High Energy Phys. 07 (2003) 047.
  11. Y. Jiang, S. Komatsu, I. Kostov, and D. Serban, Clustering and the three-point function, J. Phys. A 49, 454003 (2016).
  12. N. Gromov, F. Levkovich-Maslyuk, P. Ryan, and D. Volin, Dual separated variables and scalar products, Phys. Lett. B 806, 135494 (2020).
  13. A. Cavaglià, N. Gromov, and F. Levkovich-Maslyuk, Separation of variables and scalar products at any rank, J. High Energy Phys. 09 (2019) 052.
  14. N. Gromov, F. Levkovich-Maslyuk, and P. Ryan, Determinant form of correlators in high rank integrable spin chains via separation of variables, J. High Energy Phys. 05 (2021) 169.
  15. Ö. Gürdoğan and V. Kazakov, New integrable 4D quantum field theories from strongly deformed planar N=4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 117, 201602 (2016).
  16. A. Cavaglià, N. Gromov, and F. Levkovich-Maslyuk, Separation of variables in AdS/CFT: Functional approach for the fishnet CFT, J. High Energy Phys. 06 (2021) 131.
  17. L. D. Faddeev and G. P. Korchemsky, High-energy QCD as a completely integrable model, Phys. Lett. B 342, 311 (1995).
  18. A. V. Kotikov, A. Rej, and S. Zieme, Analytic three-loop solutions for N=4 SYM twist operators, Nucl. Phys. B813, 460 (2009); M. Beccaria, A. V. Belitsky, A. V. Kotikov, and S. Zieme, Analytic solution of the multiloop Baxter equation, B827, 565 (2010).
  19. B. Basso and A. V. Belitsky, Luescher formula for GKP string, Nucl. Phys. B860, 1 (2012).
  20. F. A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B599, 459 (2001).
  21. B. Basso and G. P. Korchemsky, Anomalous dimensions of high-spin operators beyond the leading order, Nucl. Phys. B775, 1 (2007); L. F. Alday, A. Bissi, and T. Lukowski, Large spin systematics in CFT, J. High Energy Phys. 11 (2015) 101.
  22. N. Gromov and P. Vieira, Tailoring three-point functions and integrability IV. Theta-morphism, J. High Energy Phys. 04 (2014) 068.
  23. Y. Kazama, S. Komatsu, and T. Nishimura, A new integral representation for the scalar products of Bethe states for the XXX spin chain, J. High Energy Phys. 09 (2013) 013.
  24. Y. Jiang, S. Komatsu, I. Kostov, and D. Serban, The hexagon in the mirror: The three-point function in the SoV representation, J. Phys. A 49, 174007 (2016).

  25. In this section we assume that ℓ23≥2 so that bottom mirror corrections can be neglected [3].

  26. S. Giombi and S. Komatsu, Exact correlators on the Wilson loop in N=4 SYM: Localization, Defect CFT, and integrability, J. High Energy Phys. 05 (2018) 109; 11 (2018) 123(E).
  27. S. Giombi and S. Komatsu, More exact results in the Wilson loop defect CFT: Bulk-defect OPE, nonplanar corrections and quantum spectral curve, J. Phys. A 52, 125401 (2019).
  28. N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve for a cusped Wilson line in N=4 SYM, J. High Energy Phys. 04 (2016) 134.
  29. S. Giombi, S. Komatsu, and B. Offertaler, Large charges on the Wilson loop in N=4 SYM. Part II. Quantum fluctuations, OPE, and spectral curve, J. High Energy Phys. 08 (2022) 011.
  30. J. Caetano and S. Komatsu, Functional equations and separation of variables for exact g-function, J. High Energy Phys. 09 (2020) 180.

  31. Indeed, (1) matches the perturbative solution for the μ0 function of [32] up to a factor of 2 in the exponent. What is the role of this modified μ function in the quantum spectral curve? At higher loops, a thorough investigation is needed.

  32. C. Marboe and D. Volin, Quantum spectral curve as a tool for a perturbative quantum field theory, Nucl. Phys. B899, 810 (2015).
  33. B. Basso, A. Georgoudis, and A. K. Sueiro, Structure constants of short operators in planar N=4 SYM theory, Phys. Rev. Lett. 130, 131603 (2023).
  34. L. F. Alday, B. Eden, G. P. Korchemsky, J. Maldacena, and E. Sokatchev, From correlation functions to Wilson loops, J. High Energy Phys. 09 (2011) 123.
  35. L. F. Alday, D. Gaiotto, J. Maldacena, A. Sever, and P. Vieira, An operator product expansion for polygonal null Wilson loops, J. High Energy Phys. 04 (2011) 088.
  36. C. Bercini, V. Gonçalves, A. Homrich, and P. Vieira, The Wilson loop—large spin OPE dictionary, J. High Energy Phys. 07 (2022) 079.
  37. C. Bercini, V. Gonçalves, and P. Vieira, Light-cone bootstrap of higher point functions and Wilson loop duality, Phys. Rev. Lett. 126, 121603 (2021).
  38. T. Fleury and S. Komatsu, Hexagonalization of correlation functions, J. High Energy Phys. 01 (2017) 130.
  39. F. Coronado, Perturbative four-point functions in planar N=4 SYM from hexagonalization, J. High Energy Phys. 01 (2019) 056.
  40. F. Coronado, Bootstrapping the simplest correlator in planar N=4 supersymmetric Yang-Mills theory to all loops, Phys. Rev. Lett. 124, 171601 (2020).
  41. I. Kostov, V. B. Petkova, and D. Serban, The octagon as a determinant, J. High Energy Phys. 11 (2019) 178.

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Phys. Rev. D 110, L121901– Published 2 December, 2024
  • Received 23 November 2022
  • Accepted 16 November 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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