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Correlators on non-supersymmetric Wilson line in \( \mathcal{N}=4 \) SYM and AdS2/CFT1

A preprint version of the article is available at arXiv.

Abstract

Correlators of local operators inserted on a straight or circular Wilson loop in a conformal gauge theory have the structure of a one-dimensional “defect” CFT. As was shown in arXiv:1706.00756, in the case of supersymmetric Wilson-Maldacena loop in \( \mathcal{N}=4 \) SYM one can compute the leading strong-coupling contributions to 4-point correlators of the simplest “protected” operators by starting with the AdS5 × S5 string action expanded near the AdS2 minimal surface and evaluating the corresponding tree-level AdS2 Witten diagrams. Here we perform the analogous computations in the non-supersymmetric case of the standard Wilson loop with no coupling to the scalars. The corresponding non-supersymmetric “defect” CFT1 should have an unbroken SO(6) global symmetry. The elementary bosonic operators (6 SYM scalars and 3 components of the SYM field strength) are dual respectively to the S5 embedding coordinates and AdS5 coordinates transverse to the minimal surface ending on the line at the boundary. The SO(6) symmetry is preserved on the string side provided the 5-sphere coordinates satisfy Neumann boundary conditions (as opposed to Dirichlet in the supersymmetric case); this implies that one should integrate over the S5 expansion point. The massless S5 fluctuations then have logarithmic propagator, corresponding to the boundary scalar operator having dimension \( \Delta =\frac{5}{\sqrt{\lambda }}+\dots \) at strong coupling. The resulting functions of 1d cross-ratio appearing in the 4-point functions turn out to have a more complicated structure than in the supersymmetric case, involving polylog (Li3 and Li2) functions. We also discuss consistency with the operator product expansion which allows extracting the leading strong coupling corrections to the anomalous dimensions of the operators appearing in the intermediate channels.

References

  1. L.F. Alday and J. Maldacena, Comments on gluon scattering amplitudes via AdS/CFT, JHEP 11 (2007) 068 [arXiv:0710.1060] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  2. J. Polchinski and J. Sully, Wilson Loop Renormalization Group Flows, JHEP 10 (2011) 059 [arXiv:1104.5077] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. M. Beccaria, S. Giombi and A. Tseytlin, Non-supersymmetric Wilson loop in \( \mathcal{N}=4 \) SYM and defect 1d CFT, JHEP 03 (2018) 131 [arXiv:1712.06874] [INSPIRE].

  4. A.M. Polyakov and V.S. Rychkov, Gauge field strings duality and the loop equation, Nucl. Phys. B 581 (2000) 116 [hep-th/0002106] [INSPIRE].

  5. N. Drukker and S. Kawamoto, Small deformations of supersymmetric Wilson loops and open spin-chains, JHEP 07 (2006) 024 [hep-th/0604124] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  6. M. Sakaguchi and K. Yoshida, Holography of Non-relativistic String on AdS 5 × S 5, JHEP 02 (2008) 092 [arXiv:0712.4112] [INSPIRE].

  7. N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  8. 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, JHEP 06 (2012) 048 [arXiv:1202.4455] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  9. 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].

  10. M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  11. 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].

  12. M. Kim, N. Kiryu, S. Komatsu and T. Nishimura, Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop, JHEP 12 (2017) 055 [arXiv:1710.07325] [INSPIRE].

  13. S. Giombi and S. Komatsu, Exact Correlators on the Wilson Loop in \( \mathcal{N}=4 \) SYM: Localization, Defect CFT and Integrability, JHEP 05 (2018) 109 [Erratum ibid. 11 (2018) 123] [arXiv:1802.05201] [INSPIRE].

  14. M. Kim and N. Kiryu, Structure constants of operators on the Wilson loop from integrability, JHEP 11 (2017) 116 [arXiv:1706.02989] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  15. N. Drukker, I. Shamir and C. Vergu, Defect multiplets of \( \mathcal{N}=1 \) supersymmetry in 4d, JHEP 01 (2018) 034 [arXiv:1711.03455] [INSPIRE].

  16. D. Correa, M. Leoni and S. Luque, Spin chain integrability in non-supersymmetric Wilson loops, JHEP 12 (2018) 050 [arXiv:1810.04643] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. P. Liendo, C. Meneghelli and V. Mitev, Bootstrapping the half-BPS line defect, JHEP 10 (2018) 077 [arXiv:1806.01862] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  18. M. Beccaria and A.A. Tseytlin, On non-supersymmetric generalizations of the Wilson-Maldacena loops in N = 4 SYM, Nucl. Phys. B 934 (2018) 466 [arXiv:1804.02179] [INSPIRE].

  19. L. Bianchi, M. Lemos and M. Meineri, Line Defects and Radiation in \( \mathcal{N}=2 \) Conformal Theories, Phys. Rev. Lett. 121 (2018) 141601 [arXiv:1805.04111] [INSPIRE].

  20. 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 (2019) 125401 [arXiv:1811.02369] [INSPIRE].

  21. N. Kiryu and S. Komatsu, Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization, JHEP 02 (2019) 090 [arXiv:1812.04593] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  22. D. Mazac and M.F. Paulos, The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices, JHEP 02 (2019) 162 [arXiv:1803.10233] [INSPIRE].

  23. A. Cavaglià, N. Gromov and F. Levkovich-Maslyuk, Quantum spectral curve and structure constants in \( \mathcal{N}=4 \) SYM: cusps in the ladder limit, JHEP 10 (2018) 060 [arXiv:1802.04237] [INSPIRE].

  24. S. Samuel, Color Zitterbewegung, Nucl. Phys. B 149 (1979) 517 [INSPIRE].

  25. J. Ishida and A. Hosoya, Path Integral for a Color Spin and Path Ordered Phase Factor, Prog. Theor. Phys. 62 (1979) 544 [INSPIRE].

    ADS  Article  Google Scholar 

  26. I. Ya. Arefeva, Quantum contour field equations, Phys. Lett. 93B (1980) 347 [INSPIRE].

  27. J.-L. Gervais and A. Neveu, The Slope of the Leading Regge Trajectory in Quantum Chromodynamics, Nucl. Phys. B 163 (1980) 189 [INSPIRE].

  28. J. Gomis and F. Passerini, Holographic Wilson Loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  29. C. Hoyos, A defect action for Wilson loops, JHEP 07 (2018) 045 [arXiv:1803.09809] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  30. N. Drukker, D.J. Gross and A.A. Tseytlin, Green-Schwarz string in AdS 5 × S 5 : Semiclassical partition function, JHEP 04 (2000) 021 [hep-th/0001204] [INSPIRE].

  31. A. Faraggi and L.A. Pando Zayas, The Spectrum of Excitations of Holographic Wilson Loops, JHEP 05 (2011) 018 [arXiv:1101.5145] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  32. B. Fiol, B. Garolera and G. Torrents, Exact momentum fluctuations of an accelerated quark in N = 4 super Yang-Mills, JHEP 06 (2013) 011 [arXiv:1302.6991] [INSPIRE].

  33. D. Carmi, L. Di Pietro and S. Komatsu, A Study of Quantum Field Theories in AdS at Finite Coupling, JHEP 01 (2019) 200 [arXiv:1810.04185] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  34. I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].

  35. 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].

  36. D. Medina-Rincon, A.A. Tseytlin and K. Zarembo, Precision matching of circular Wilson loops and strings in AdS 5 × S 5, JHEP 05 (2018) 199 [arXiv:1804.08925] [INSPIRE].

  37. S. Elitzur, The Applicability of Perturbation Expansion to Two-dimensional Goldstone Systems, Nucl. Phys. B 212 (1983) 501 [INSPIRE].

  38. F. David, Cancellations of Infrared Divergences in the Two-dimensional Nonlinear σ-models, Commun. Math. Phys. 81 (1981) 149 [INSPIRE].

  39. J.L. Miramontes and J.M. Sanchez de Santos, Are there infrared problems in the 2-d nonlinear σ -models?, Phys. Lett. B 246 (1990) 399 [INSPIRE].

  40. J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  41. A. Dekel, Wilson Loops and Minimal Surfaces Beyond the Wavy Approximation, JHEP 03 (2015) 085 [arXiv:1501.04202] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  42. R. Ishizeki, M. Kruczenski and S. Ziama, Notes on Euclidean Wilson loops and Riemann Theta functions, Phys. Rev. D 85 (2012) 106004 [arXiv:1104.3567] [INSPIRE].

  43. F.A. Dolan and H. Osborn, Conformal Partial Waves: Further Mathematical Results, arXiv:1108.6194 [INSPIRE].

  44. J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].

  45. J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  46. J. de Boer, E. Llabrés, J.F. Pedraza and D. Vegh, Chaotic strings in AdS/CFT, Phys. Rev. Lett. 120 (2018) 201604 [arXiv:1709.01052] [INSPIRE].

    ADS  Article  Google Scholar 

  47. S. Dubovsky, R. Flauger and V. Gorbenko, Solving the Simplest Theory of Quantum Gravity, JHEP 09 (2012) 133 [arXiv:1205.6805] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  48. E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, in Strings, Branes and Extra Dimensions: TASI 2001: Proceedings, pp. 3-158, 2002, hep-th/0201253 [INSPIRE].

  49. M. Hogervorst and B.C. van Rees, Crossing symmetry in alpha space, JHEP 11 (2017) 193 [arXiv:1702.08471] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  50. A.A. Tseytlin, On semiclassical approximation and spinning string vertex operators in AdS 5 × S 5, Nucl. Phys. B 664 (2003) 247 [hep-th/0304139] [INSPIRE].

  51. I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from Conformal Field Theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  52. A.L. Fitzpatrick and J. Kaplan, Unitarity and the Holographic S-matrix, JHEP 10 (2012) 032 [arXiv:1112.4845] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  53. E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].

  54. F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].

  55. G. Arutyunov, F.A. Dolan, H. Osborn and E. Sokatchev, Correlation functions and massive Kaluza-Klein modes in the AdS/CFT correspondence, Nucl. Phys. B 665 (2003) 273 [hep-th/0212116] [INSPIRE].

  56. S. Randjbar-Daemi, A. Salam and J.A. Strathdee, σ-Models and String Theories, Int. J. Mod. Phys. A 2 (1987) 667 [INSPIRE].

  57. A.M. Polyakov, Quantum Geometry of Bosonic Strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].

  58. R.I. Nepomechie, Duality of the Polyakov N Point Amplitude, Phys. Rev. D 25 (1982) 2706 [INSPIRE].

  59. E.S. Fradkin and A.A. Tseytlin, Quantum String Theory Effective Action, Nucl. Phys. B 261 (1985) 1 [Erratum ibid. B 269 (1986) 745] [INSPIRE].

  60. B. Durhuus, H.B. Nielsen, P. Olesen and J.L. Petersen, Dual models as saddle point approximations to Polyakovs quantized string, Nucl. Phys. B 196 (1982) 498 [INSPIRE].

  61. S.N. Solodukhin, Correlation functions of boundary field theory from bulk Greens functions and phases in the boundary theory, Nucl. Phys. B 539 (1999) 403 [hep-th/9806004] [INSPIRE].

  62. A.A. Tseytlin, Graviton amplitudes, effective action and string generating functional on the disk, Int. J. Mod. Phys. A 4 (1989) 3269 [INSPIRE].

  63. S.P. de Alwis, The Dilaton Vertex in the Path Integral Formulation of Strings, Phys. Lett. 168B (1986) 59 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  64. A.A. Tseytlin, Renormalization of String Loop Corrections on the Disk and the Annulus, Phys. Lett. B 208 (1988) 228 [INSPIRE].

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Correspondence to Matteo Beccaria.

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Beccaria, M., Giombi, S. & Tseytlin, A.A. Correlators on non-supersymmetric Wilson line in \( \mathcal{N}=4 \) SYM and AdS2/CFT1. J. High Energ. Phys. 2019, 122 (2019). https://doi.org/10.1007/JHEP05(2019)122

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Keywords

  • AdS-CFT Correspondence
  • Conformal Field Theory