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  • Letter
  • Open Access

Integrability and conformal bootstrap: One dimensional defect conformal field theory

Andrea Cavaglià1,*, Nikolay Gromov1,2,†, Julius Julius1,‡, and Michelangelo Preti1,§

  • 1Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom
  • 2St. Petersburg INP, Gatchina, 188 300 St. Petersburg, Russia

  • *andrea.cavaglia@kcl.ac.uk
  • †nikolay.gromov@kcl.ac.uk
  • ‡julius.julius@kcl.ac.uk
  • §michelangelo.preti@kcl.ac.uk

Phys. Rev. D 105, L021902 – Published 7 January, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.L021902

Abstract

In this paper we study how the exact nonperturbative integrability methods in 4D N=4 super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access previously unreachable quantities such as correlation functions at finite coupling. In the setup of 1D defect conformal field theory living on a Maldacena-Wilson line, we managed to compute with good precision a nonsupersymmetric structure constant for a wide range of the ‘t Hooft coupling. Our result is particularly precise at strong coupling and matches well with the recent analytic results of Meneghelli and Ferrero.

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References (60)

  1. 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).
  2. N. Gromov, V. Kazakov, S. Leurent, and D. Volin, Quantum spectral curve for arbitrary state/operator in AdS5/CFT4, J. High Energy Phys. 09 (2015) 187.
  3. N. Gromov, F. Levkovich-Maslyuk, and G. Sizov, Pomeron Eigenvalue at Three Loops in N=4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 115, 251601 (2015).
  4. B. Basso, S. Komatsu, and P. Vieira, Structure constants and integrable bootstrap in planar N=4 SYM theory, arXiv:1505.06745.
  5. A. Cavaglià, N. Gromov, and F. Levkovich-Maslyuk, Quantum spectral curve and structure constants in N=4 SYM: Cusps in the ladder limit, J. High Energy Phys. 10 (2018) 060.
  6. Y. Jiang, S. Komatsu, and E. Vescovi, Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 123, 191601 (2019).
  7. 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.
  8. D. Simmons-Duffin, The conformal bootstrap, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (World Scientific, Singapore, 2016).
  9. D. Poland, S. Rychkov, and A. Vichi, The conformal bootstrap: Theory, numerical techniques, and applications, Rev. Mod. Phys. 91, 015002 (2019).
  10. S. M. Chester, Weizmann lectures on the numerical conformal bootstrap, arXiv:1907.05147.
  11. P. Liendo, C. Meneghelli, and V. Mitev, Bootstrapping the half-BPS line defect, J. High Energy Phys. 10 (2018) 077.
  12. C. Beem, L. Rastelli, and B. C. van Rees, More N=4 superconformal bootstrap, Phys. Rev. D 96, 046014 (2017).
  13. F. Gliozzi, P. Liendo, M. Meineri, and A. Rago, Boundary and interface CFTs from the conformal bootstrap, J. High Energy Phys. 05 (2015) 036.
  14. F. Gliozzi, Truncatable bootstrap equations in algebraic form and critical surface exponents, J. High Energy Phys. 10 (2016) 037.
  15. Y. Nakayama, Bootstrapping Critical Ising Model on Three-Dimensional Real Projective Space, Phys. Rev. Lett. 116, 141602 (2016).
  16. M. Picco, S. Ribault, and R. Santachiara, A conformal bootstrap approach to critical percolation in two dimensions, SciPost Phys. 1, 009 (2016).
  17. Y. He, J. L. Jacobsen, and H. Saleur, Geometrical four-point functions in the two-dimensional critical Q-state Potts model: The interchiral conformal bootstrap, J. High Energy Phys. 12 (2020) 019.
  18. N. Kiryu and S. Komatsu, Correlation functions on the Half-BPS Wilson loop: Perturbation and hexagonalization, J. High Energy Phys. 02 (2019) 090.
  19. A. Cavaglià, N. Gromov, J. Julius, and M. Preti (to be published).
  20. S. Giombi, R. Roiban, and A. A. Tseytlin, Half-BPS Wilson loop and AdS2/CFT1, Nucl. Phys. B922, 499 (2017).
  21. P. Ferrero and C. Meneghelli, Bootstrapping the half-BPS line defect CFT in N=4 SYM at strong coupling, Phys. Rev. D 104, L081703 (2021).
  22. 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).
  23. J. M. Maldacena, Wilson Loops in Large N Field Theories, Phys. Rev. Lett. 80, 4859 (1998).
  24. J. K. Erickson, G. W. Semenoff, and K. Zarembo, Wilson loops in N=4 supersymmetric Yang-Mills theory, Nucl. Phys. B582, 155 (2000).
  25. P. Liendo and C. Meneghelli, Bootstrap equations for N=4 SYM with defects, J. High Energy Phys. 01 (2017) 122.
  26. L. Bianchi, L. Griguolo, M. Preti, and D. Seminara, Wilson lines as superconformal defects in ABJM theory: A formula for the emitted radiation, J. High Energy Phys. 10 (2017) 050.
  27. L. Bianchi, M. Preti, and E. Vescovi, Exact Bremsstrahlung functions in ABJM theory, J. High Energy Phys. 07 (2018) 060.
  28. L. Bianchi, G. Bliard, V. Forini, L. Griguolo, and D. Seminara, Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1, J. High Energy Phys. 08 (2020) 143.
  29. The QSC is known for the spectrum of local operators in ABJM theory [30, 31], but its version for the defect CFT is still unknown.

  30. A. Cavaglià, D. Fioravanti, N. Gromov, and R. Tateo, Quantum Spectral Curve of the N=6 Supersymmetric Chern-Simons Theory, Phys. Rev. Lett. 113, 021601 (2014).
  31. D. Bombardelli, A. Cavaglià, D. Fioravanti, N. Gromov, and R. Tateo, The full quantum spectral curve for AdS4/CFT3, J. High Energy Phys. 09 (2017) 140.
  32. N. Drukker and S. Kawamoto, Small deformations of supersymmetric Wilson loops and open spin-chains, J. High Energy Phys. 07 (2006) 024.
  33. N. Drukker, Integrable Wilson loops, J. High Energy Phys. 10 (2013) 135.
  34. D. Correa, J. Henn, J. Maldacena, and A. Sever, An exact formula for the radiation of a moving quark in N=4 super Yang Mills, J. High Energy Phys. 06 (2012) 048.
  35. M. Bonini, L. Griguolo, M. Preti, and D. Seminara, Bremsstrahlung function, leading Lüscher correction at weak coupling and localization, J. High Energy Phys. 02 (2016) 172.
  36. M. Cooke, A. Dekel, and N. Drukker, The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines, J. Phys. A 50, 335401 (2017).
  37. 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).
  38. D. Grabner, N. Gromov, and J. Julius, Excited states of one-dimensional defect CFTs from the quantum spectral curve, J. High Energy Phys. 07 (2020) 042.
  39. D. Correa, J. Maldacena, and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, J. High Energy Phys. 08 (2012) 134,
  40. 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.
  41. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.105.L021902 for explicit numerical data to support the claims of the paper.
  42. N. Gromov, Introduction to the spectrum of N=4 SYM and the quantum spectral curve, arXiv:1708.03648.
  43. V. Kazakov, Quantum spectral curve of γ-twisted N=4 SYM theory and fishnet CFT, Rev. Math. Phys. 30, 1840010 (2018).
  44. F. Levkovich-Maslyuk, A review of the AdS/CFT quantum spectral curve, J. Phys. A 53, 283004 (2020).
  45. C. Marboe and D. Volin, Quantum spectral curve as a tool for a perturbative quantum field theory, Nucl. Phys. B899, 810 (2015).
  46. C. Marboe and D. Volin, The full spectrum of AdS5/CFT4 II: Weak coupling expansion via the quantum spectral curve, J. Phys. A 54, 055201 (2021).
  47. D. Correa, M. Leoni, and S. Luque, Spin chain integrability in nonsupersymmetric Wilson loops, J. High Energy Phys. 12 (2018) 050.
  48. I. Bars and M. Gunaydin, Unitary representations of noncompact supergroups, Commun. Math. Phys. 91, 31 (1983).
  49. M. Gunaydin and N. Marcus, The spectrum of the S5 compactification of the chiral N=2, D=10 supergravity and the unitary supermultiplets of U(2,2/4), Classical Quantum Gravity 2, L11 (1985).
  50. N. Beisert, The complete one loop dilatation operator of N=4 super-Yang-Mills theory, Nucl. Phys. B676, 3 (2004).
  51. N. Beisert, The dilatation operator of N=4 super Yang-Mills theory and integrability, Phys. Rep. 405, 1 (2004).
  52. C. Marboe and D. Volin, The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system, J. Phys. A 51, 165401 (2018).
  53. N. Gromov, F. Levkovich-Maslyuk, and G. Sizov, Quantum spectral curve and the numerical solution of the spectral problem in AdS5/CFT4, J. High Energy Phys. 06 (2016) 036.
  54. L. F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, J. High Energy Phys. 11 (2007) 068.
  55. C. Meneghelli, Proceedings of the London Integrability Journal Club (2020), https://youtu.be/kst1zikjpi8.
  56. P. S. Howe and P. C. West, AdS/SCFT in superspace, Classical Quantum Gravity 18, 3143 (2001).
  57. N. Drukker and D. J. Gross, An exact prediction of N=4 SUSYM theory for string theory, J. Math. Phys. (N.Y.) 42, 2896 (2001).
  58. V. Pestun, Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops, J. High Energy Phys. 12 (2012) 067.
  59. D. Simmons-Duffin, A semidefinite program solver for the conformal bootstrap, J. High Energy Phys. 06 (2015) 174.
  60. W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB, arXiv:1909.09745.

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