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Journal of High Energy Physics

, 2017:55 | Cite as

Structure constants of defect changing operators on the 1/2 BPS Wilson loop

  • Minkyoo Kim
  • Naoki Kiryu
  • Shota KomatsuEmail author
  • Takuya Nishimura
Open Access
Regular Article - Theoretical Physics

Abstract

We study three-point functions of operators on the 1/2 BPS Wilson loop in planar \( \mathcal{N} \) = 4 super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the \( \mathrm{S}\mathrm{L}\left(2,\mathbb{R}\right) \) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.

Keywords

1/N Expansion Conformal Field Theory AdS-CFT Correspondence Integrable Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    M. Billo, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].MathSciNetADSGoogle Scholar
  2. [2]
    A. Gadde, Conformal constraints on defects, arXiv:1602.06354 [INSPIRE].
  3. [3]
    N. Drukker, Integrable Wilson loops, JHEP 10 (2013) 135 [arXiv:1203.1617] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  4. [4]
    D. Correa, J. Maldacena and A. Sever, The quark anti-quark potential and the cusp anomalous dimension from a TBA equation, JHEP 08 (2012) 134 [arXiv:1203.1913] [INSPIRE].CrossRefADSGoogle Scholar
  5. [5]
    N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve for a cusped Wilson line in \( \mathcal{N} \) = 4 SYM, JHEP 04 (2016) 134 [arXiv:1510.02098] [INSPIRE].ADSGoogle Scholar
  6. [6]
    M. Cooke, A. Dekel and N. Drukker, The Wilson loop CFT: insertion dimensions and structure constants from wavy lines, J. Phys. A 50 (2017) 335401 [arXiv:1703.03812] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  7. [7]
    S. Giombi, R. Roiban and A.A. Tseytlin, Half-BPS Wilson loop and AdS 2 /CFT 1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [INSPIRE].CrossRefzbMATHGoogle Scholar
  8. [8]
    B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory, arXiv:1505.06745 [INSPIRE].
  9. [9]
    D. Correa, J. Henn, J. Maldacena and A. Sever, The cusp anomalous dimension at three loops and beyond, JHEP 05 (2012) 098 [arXiv:1203.1019] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  10. [10]
    A. Cavaglia, N. Gromov and F. Levkovich-Maslyuk, to appear.Google Scholar
  11. [11]
    N. Drukker and S. Kawamoto, Small deformations of supersymmetric Wilson loops and open spin-chains, JHEP 07 (2006) 024 [hep-th/0604124] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  12. [12]
    J.K. Erickson, G.W. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  13. [13]
    N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].CrossRefzbMATHADSGoogle Scholar
  14. [14]
    N. Drukker and J. Plefka, The structure of n-point functions of chiral primary operators in N = 4 super Yang-Mills at one-loop, JHEP 04 (2009) 001 [arXiv:0812.3341] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  15. [15]
    S. Giombi, C. Sleight and M. Taronna, Spinning AdS loop diagrams: two point functions, arXiv:1708.08404 [INSPIRE].
  16. [16]
    J.K. Erickson, G.W. Semenoff, R.J. Szabo and K. Zarembo, Static potential in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 61 (2000) 105006 [hep-th/9911088] [INSPIRE].MathSciNetADSGoogle Scholar
  17. [17]
    M. Kim and N. Kiryu, Structure constants of operators on the Wilson loop from integrability, JHEP 11 (2017) 116 [arXiv:1706.02989] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  18. [18]
    Z. Bajnok and L. Hollo, On form factors of boundary changing operators, Nucl. Phys. B 905 (2016) 96 [arXiv:1510.08232] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  19. [19]
    N. Gromov and F. Levkovich-Maslyuk, Quark-anti-quark potential in \( \mathcal{N} \) = 4 SYM, JHEP 12 (2016) 122 [arXiv:1601.05679] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    O. Gurdogan and V. Kazakov, New integrable 4D quantum field theories from strongly deformed planar \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory, Phys. Rev. Lett. 117 (2016) 201602 [arXiv:1512.06704] [INSPIRE].MathSciNetCrossRefADSGoogle Scholar
  21. [21]
    J. Caetano, O. Gurdogan and V. Kazakov, Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs, arXiv:1612.05895 [INSPIRE].
  22. [22]
    O. Mamroud and G. Torrents, RG stability of integrable fishnet models, JHEP 06 (2017) 012 [arXiv:1703.04152] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  23. [23]
    D. Chicherin, V. Kazakov, F. Loebbert, D. Müller and D.-l. Zhong, Yangian symmetry for bi-scalar loop amplitudes, arXiv:1704.01967 [INSPIRE].
  24. [24]
    N. Gromov et al., Integrability of conformal fishnet theory, arXiv:1706.04167 [INSPIRE].
  25. [25]
    D. Chicherin et al., Yangian symmetry for fishnet Feynman graphs, arXiv:1708.00007 [INSPIRE].
  26. [26]
    D.J. Gross and V. Rosenhaus, The bulk dual of SYK: cubic couplings, JHEP 05 (2017) 092 [arXiv:1702.08016] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  27. [27]
    D.J. Gross and V. Rosenhaus, A line of CFTs: from generalized free fields to SYK, JHEP 07 (2017) 086 [arXiv:1706.07015] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  28. [28]
    N. Beisert, C. Kristjansen, J. Plefka, G.W. Semenoff and M. Staudacher, BMN correlators and operator mixing in N = 4 super Yang-Mills theory, Nucl. Phys. B 650 (2003) 125 [hep-th/0208178] [INSPIRE].MathSciNetCrossRefzbMATHADSGoogle Scholar
  29. [29]
    N.I. Usyukina and A.I. Davydychev, An approach to the evaluation of three and four point ladder diagrams, Phys. Lett. B 298 (1993) 363 [INSPIRE].CrossRefADSGoogle Scholar
  30. [30]
    C. Chamon, R. Jackiw, S.-Y. Pi and L. Santos, Conformal quantum mechanics as the CFT 1 dual to AdS 2, Phys. Lett. B 701 (2011) 503 [arXiv:1106.0726] [INSPIRE].CrossRefGoogle Scholar
  31. [31]
    S.H. Dong and R. Lemus, A new dynamical group approach to the modified Poschl-Teller potential, quant-ph/0110157.

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Minkyoo Kim
    • 1
    • 2
  • Naoki Kiryu
    • 3
  • Shota Komatsu
    • 4
    • 5
    Email author
  • Takuya Nishimura
    • 3
  1. 1.National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical PhysicsUniversity of the WitwatersrandJohannesburg WitsSouth Africa
  2. 2.MTA Lendulet Holographic QFT Group, Wigner Research CentreBudapestHungary
  3. 3.Institute of PhysicsUniversity of TokyoTokyoJapan
  4. 4.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  5. 5.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.

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