Skip to main content
Log in

Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

We review the role of integrability in certain aspects of \({\fancyscript{N}=4}\) SYM which go beyond the planar spectrum. In particular, we discuss integrability in relation to non-planar anomalous dimensions, multi-point functions and Maldacena–Wilson loops.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Minahan J.A., Zarembo K.: The Bethe-ansatz for \({\fancyscript{N}=4}\) super Yang-Mills. JHEP 0303, 013 (2003). doi:10.1088/1126-6708/2003/03/013 (arXiv:hep-th/0212208)

    MathSciNet  ADS  Google Scholar 

  2. Beisert N., Kristjansen C., Staudacher M.: The dilatation operator of \({\fancyscript{N}=4}\) super Yang-Mills theory. Nucl. Phys. B 664, 131 (2003). doi:10.1016/S0550-3213(03)00406-1 (arXiv:hep-th/0303060)

    MathSciNet  ADS  MATH  Google Scholar 

  3. Mandal G., Suryanarayana N.V., Wadia S.R.: Aspects of semiclassical strings in AdS 5. Phys. Lett. B 543, 81 (2002). doi:10.1016/S0370-2693(02)02424-3 (arXiv:hep-th/0206103)

    MathSciNet  ADS  MATH  Google Scholar 

  4. Bena I., Polchinski J., Roiban R.: Hidden symmetries of the AdS 5 × S 5 superstring. Phys. Rev. D 69, 046002 (2004) doi:10.1103/PhysRevD.69.046002 (arXiv:hep-th/0305116)

    MathSciNet  ADS  Google Scholar 

  5. Zoubos, K.: Review of AdS/CFT integrability, Chapter IV.2: deformations, orbifolds and open boundaries. Lett. Math. Phys. Published in this volume. arXiv:1012.3998

  6. Korchemsky, G.: Review of AdS/CFT integrability, Chapter IV.4: integrability in QCD and \({\fancyscript{N} < 4}\) SYM. Lett. Math. Phys. Published in this volume. arXiv:1012.4000

  7. Roiban, R.: Review of AdS/CFT integrability, Chapter V.1: scattering amplitudes—a brief introduction. Lett. Math. Phys. Published in this volume. arXiv:1012.4001

  8. Drummond, J.M.: Review of AdS/CFT integrability, Chapter V.2: dual superconformal symmetry. Lett. Math. Phys. Published in this volume. arXiv:1012.4002

  9. Alday, L.F.: Review of AdS/CFT integrability, Chapter V.3: scattering amplitudes at strong coupling. Lett. Math. Phys. Published in this volume. arXiv:1012.4003

  10. Sieg, C.: Review of AdS/CFT integrability, Chapter I.2: the spectrum from perturbative gauge theory. Lett. Math. Phys. Published in this volume. arXiv:1012.3984

  11. Beisert N., Kristjansen C., Plefka J., Semenoff G.W., Staudacher M.: BMN correlators and operator mixing in \({\fancyscript{N}=4}\) super Yang-Mills theory. Nucl. Phys. B 650, 125 (2003) doi:10.1016/S0550-3213(02)01025-8 (arXiv:hep-th/0208178)

    MathSciNet  ADS  MATH  Google Scholar 

  12. Beisert N., Kristjansen C., Plefka J., Staudacher M.: BMN gauge theory as a quantum mechanical system. Phys. Lett. B 558, 229 (2003) doi:10.1016/S0370-2693(03)00269-7 (arXiv:hep-th/0212269)

    MathSciNet  ADS  MATH  Google Scholar 

  13. Constable N.R. et al.: PP-wave string interactions from perturbative Yang-Mills theory. JHEP. 0207, 017 (2002) doi:10.1088/1126-6708/2002/07/017 (arXiv:hep-th/0205089)

    MathSciNet  ADS  Google Scholar 

  14. Beisert N.: The complete one-loop dilatation operator of \({\fancyscript{N}=4}\) super Yang-Mills theory. Nucl. Phys. B 676, 3 (2004) doi:10.1016/j.nuclphysb.2003.10.019 (arXiv:hep-th/0307015)

    MathSciNet  ADS  MATH  Google Scholar 

  15. Zwiebel B.I.: \({\fancyscript{N}=4}\) SYM to two loops: compact expressions for the non-compact symmetry algebra of the su(1, 1/2) sector. JHEP. 0602, 055 (2006) doi:10.1088/1126-6708/2006/02/055 (arXiv:hep-th/0511109)

    MathSciNet  ADS  Google Scholar 

  16. Xiao Z.: BMN operators with a scalar fermion pair and operator mixing in \({\fancyscript{N}=4}\) Super Yang-Mills Theory. Phys. Rev. D 81, 026004 (2010) doi:10.1103/PhysRevD.81.026004 (arXiv:arXiv:0910.3390)

    MathSciNet  ADS  Google Scholar 

  17. De Risi G., Grignani G., Orselli M., Semenoff G.W.: DLCQ string spectrum from \({\fancyscript{N}=2}\) SYM theory. JHEP. 0411, 053 (2004) doi:10.1088/1126-6708/2004/11/053 (arXiv:hep-th/0409315)

    MathSciNet  ADS  Google Scholar 

  18. Aharony O., Bergman O., Jafferis D.L., Maldacena J.: \({\fancyscript{N}=6}\) superconformal Chern-Simons-matter theories, M2-branes and their gravity duals. JHEP. 0810, 091 (2008) doi:10.1088/1126-6708/2008/10/091 (arXiv:0806.1218)

    MathSciNet  ADS  Google Scholar 

  19. Aharony O., Bergman O., Jafferis D.L.: Fractional M2-branes. JHEP 0811, 043 (2008) doi:10.1088/1126-6708/2008/11/043 (arXiv:0807.4924)

    MathSciNet  ADS  Google Scholar 

  20. Kristjansen C., Orselli M., Zoubos K.: Non-planar ABJM Theory and Integrability. JHEP. 0903, 037 (2009) doi:10.1088/1126-6708/2009/03/037 (arXiv:0811.2150)

    MathSciNet  ADS  Google Scholar 

  21. Caputa P., Kristjansen C., Zoubos K.: Non-planar ABJ theory and parity. Phys. Lett. B 677, 197 (2009) doi:10.1016/j.physletb.2009.05.021 (arXiv:0903.3354)

    MathSciNet  ADS  Google Scholar 

  22. Janik, R.: Review of AdS/CFT integrability, Chapter III.5: Lüscher corrections. Lett. Math. Phys. Published in this volume. arXiv:1012.3994

  23. Bajnok, Z.: Review of AdS/CFT integrability, Chapter III.6: thermodynamic Bethe Ansatz. Lett. Math. Phys. Published in this volume. arXiv:1012.3995

  24. Kazakov, V., Gromov, N.: Review of AdS/CFT integrability, Chapter III.7: Hirota dynamics for quantum integrability. Lett. Math. Phys. Published in this volume. arXiv:1012.3996

  25. Sieg C., Torrielli A.: Wrapping interactions and the genus expansion of the 2-point function of composite operators. Nucl. Phys. B 723, 3 (2005) doi:10.1016/j.nuclphysb.2005.06.011 (arXiv:hep-th/0505071)

    MathSciNet  ADS  MATH  Google Scholar 

  26. Bellucci S., Casteill P.Y., Morales J.F., Sochichiu C.: Spin bit models from non-planar \({\fancyscript{N}=4}\) SYM. Nucl. Phys. B 699, 151 (2004) doi:10.1016/j.nuclphysb.2004.07.025 (arXiv:hep-th/0404066)

    MathSciNet  ADS  MATH  Google Scholar 

  27. Peeters K., Plefka J., Zamaklar M.: Splitting spinning strings in AdS/CFT. JHEP 0411, 054 (2004) doi:10.1088/1126-6708/2004/11/054 (arXiv:hep-th/0410275)

    MathSciNet  ADS  Google Scholar 

  28. Caputa P., Kristjansen C., Zoubos K.: On the spectral problem of \({\fancyscript{N}=4}\) SYM with orthogonal or symplectic gauge group. JHEP. 1010, 082 (2010) doi:10.1007/JHEP10(2010)082 (arXiv:1005.2611)

    MathSciNet  ADS  Google Scholar 

  29. Gross, D.J., Mikhailov, A., Roiban, R.: A calculation of the plane wave string Hamiltonian from \({\fancyscript{N}=4}\) super-Yang-Mills theory. JHEP 0305, 025 (2003) doi:10.1088/1126-6708/2003/05/025 (arXiv:hep-th/0208231)

    ADS  Google Scholar 

  30. Janik R.A.: BMN operators and string field theory. Phys. Lett. B 549, 237 (2002) doi:10.1016/S0370-2693(02)02908-8 (arXiv:hep-th/0209263)

    MathSciNet  ADS  MATH  Google Scholar 

  31. Beisert N., Staudacher M.: Long-range PSU(2,2/4) Bethe ansaetze for gauge theory and strings. Nucl. Phys. B 727, 1 (2005) doi:10.1016/j.nuclphysb.2005.06.038 (arXiv:hep-th/0504190)

    MathSciNet  ADS  MATH  Google Scholar 

  32. Beisert N., Eden B., Staudacher M.: Transcendentality and crossing. J. Stat. Mech. 0701, P021 (2007) arXiv:hep-th/0610251

    Google Scholar 

  33. Beisert N., Hernandez R., Lopez E.: A crossing-symmetric phase for AdS 5 × S 5 strings. JHEP 0611, 070 (2006) doi:10.1088/1126-6708/2006/11/070 (arXiv:hep-th/0609044)

    MathSciNet  ADS  Google Scholar 

  34. Doikou, A., Nepomechie, R.I.: Parity and charge conjugation symmetries and S matrix of the XXZ chain. arXiv:hep-th/9810034

  35. de Mello Koch R., Dey T.K., Ives N., Stephanou M.: Hints of integrability beyond the planar limit. JHEP. 1001, 014 (2010) doi:10.1007/JHEP01(2010)014 (arXiv:0911.0967)

    Google Scholar 

  36. Penati S., Santambrogio A.: Superspace approach to anomalous dimensions in \({\fancyscript{N}=4}\) SYM. Nucl. Phys. B 614, 367 (2001). doi:10.1016/S0550-3213(01)00414-X (arXiv:hep-th/0107071)

    MathSciNet  ADS  MATH  Google Scholar 

  37. Ryzhov A.V.: Quarter BPS operators in \({\fancyscript{N}=4}\) SYM. JHEP 0111, 046 (2001). doi:10.1088/1126-708/2001/11/046 (arXiv:hep-th/0109064)

    MathSciNet  ADS  Google Scholar 

  38. Bianchi M., Eden B., Rossi G., Stanev Y.S.: On operator mixing in \({\fancyscript{N}=4}\) SYM. Nucl. Phys. B 646, 69 (2002). doi:10.1016/S0550-3213(02)00817-9 (arXiv:hep-th/0205321)

    MathSciNet  ADS  MATH  Google Scholar 

  39. Arutyunov G., Penati S., Petkou A.C., Santambrogio A., Sokatchev E.: Non-protected operators in \({\fancyscript{N}=4}\) SYM and multiparticle states of AdS 5 SUGRA. Nucl. Phys. B 643, 49 (2002). doi:10.1016/S0550-3213(02)00679-X (arXiv:hep-th/0206020)

    MathSciNet  ADS  MATH  Google Scholar 

  40. Berenstein D.E., Maldacena J.M., Nastase H.S.: Strings in flat space and pp waves from \({\fancyscript{N}=4}\) super Yang Mills. JHEP 0204, 013 (2002). doi:10.1088/1126-6708/2002/04/013 (arXiv:hep-th/0202021)

    MathSciNet  ADS  Google Scholar 

  41. Freedman D.Z., Gursoy U.: Instability and degeneracy in the BMN correspondence. JHEP 0308, 027 (2003). doi:10.1088/1126-6708/2003/08/027 (arXiv:hep-th/0305016)

    MathSciNet  ADS  Google Scholar 

  42. Kristjansen C.: Quantum mechanics, random matrices and BMN gauge theory. Acta Phys. Polon. B 34, 4949 (2003) (arXiv:hep-th/0307204)

    MathSciNet  ADS  MATH  Google Scholar 

  43. Gutjahr P., Plefka J.: Decay widths of three-impurity states in the BMN correspondence. Nucl. Phys. B 692, 110 (2004). doi:10.1016/j.nuclphysb.2004.05.027 (arXiv:hep-th/0402211)

    MathSciNet  ADS  MATH  Google Scholar 

  44. Constable N.R., Freedman D.Z., Headrick M., Minwalla S.: Operator mixing and the BMN correspondence. JHEP 0210, 068 (2002). doi:10.1088/1126-6708/2002/10/068 (arXiv:hep-th/0209002)

    MathSciNet  ADS  Google Scholar 

  45. Gursoy U.: Vector operators in the BMN correspondence. JHEP 0307, 048 (2003). doi:10.1088/1126-6708/2003/07/048 (arXiv:hep-th/0208041)

    MathSciNet  ADS  Google Scholar 

  46. Casteill P.Y., Janik R.A., Jarosz A., Kristjansen C.: Quasilocality of joining/splitting strings from coherent states. JHEP 0712, 069 (2007). doi:10.1088/1126-6708/2007/12/069 (arXiv:0710.4166)

    MathSciNet  ADS  Google Scholar 

  47. D’Hoker E., Freedman D.Z., Skiba W.: Field theory tests for correlators in the AdS/CFT correspondence. Phys. Rev. D 59, 045008 (1999). doi:10.1103/PhysRevD.59.045008 (arXiv:hep-th/9807098)

    MathSciNet  ADS  Google Scholar 

  48. Kimura Y.: Quarter BPS classified by Brauer algebra. JHEP 1005, 103 (2010). doi:10.1007/JHEP05(2010)103 (arXiv:1002.2424)

    ADS  Google Scholar 

  49. Brown T.W.: Cut-and-join operators and \({\fancyscript{N}=4}\) super Yang-Mills. JHEP 1005, 058 (2010). doi:10.1007/JHEP05(2010)058 (arXiv:1002.2099)

    ADS  Google Scholar 

  50. Pankiewicz A.: Strings in plane wave backgrounds. Fortsch. Phys. 51, 1139 (2003). doi:10.1002/prop.200310119 (arXiv:hep-th/0307027)

    MathSciNet  ADS  Google Scholar 

  51. Plefka J.C.: Lectures on the plane-wave string / gauge theory duality. Fortsch. Phys. 52, 264 (2004). doi:10.1002/prop.200310121 (arXiv:hep-th/0307101)

    MathSciNet  ADS  MATH  Google Scholar 

  52. Spradlin, M. Volovich, A.: Light-cone string field theory in a plane wave. arXiv:hep-th/0310033

  53. Sadri D., Sheikh-Jabbari M.M.: The plane-wave/super Yang-Mills duality. Rev. Mod. Phys. 76, 853 (2004). doi:10.1103/RevModPhys.76.853 (arXiv:hep-th/0310119)

    MathSciNet  ADS  MATH  Google Scholar 

  54. Russo R., Tanzini A.: The duality between IIB string theory on pp-wave and \({\fancyscript{N}=4}\) SYM: a status report. Class. Quant. Grav. 21, S1265 (2004) arXiv:hep-th/0401155

    MathSciNet  ADS  Google Scholar 

  55. Grignani G., Orselli M., Ramadanovic B., Semenoff G.W., Young D.: AdS/CFT vs. string loops. JHEP 0606, 040 (2006). doi:10.1088/1126-6708/2006/06/040 (arXiv:hep-th/0605080)

    MathSciNet  ADS  Google Scholar 

  56. Beisert N., Tseytlin A.A.: On quantum corrections to spinning strings and Bethe equations. Phys. Lett. B 629, 102 (2005). doi:10.1016/j.physletb.2005.09.054 (arXiv:hep-th/0509084)

    MathSciNet  ADS  Google Scholar 

  57. Eden B., Staudacher M.: Integrability and transcendentality. J. Stat. Mech. 0611, P014 (2006) arXiv:hep-th/0603157

    Google Scholar 

  58. Bern Z., Czakon M., Dixon L.J., Kosower D.A., Smirnov V.A.: The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory. Phys. Rev. D 75, 085010 (2007). doi:10.1103/PhysRevD.75.085010 (arXiv:hep-th/0610248)

    MathSciNet  ADS  Google Scholar 

  59. D’Hoker, E., Freedman, D.Z.: Supersymmetric gauge theories and the AdS/CFT correspondence. arXiv:hep-th/0201253

  60. Beisert N.: BMN operators and superconformal symmetry. Nucl. Phys. B 659, 79 (2003). doi:10.1016/S0550-3213(03)00229-3 (arXiv:hep-th/0211032)

    MathSciNet  ADS  MATH  Google Scholar 

  61. D’Hoker, E., Freedman, D.Z., Mathur, S.D., Matusis, A., Rastelli, L.: Extremal correlators in the AdS/CFT correspondence. arXiv:hep-th/9908160

  62. Kristjansen C., Plefka J., Semenoff G.W., Staudacher M.: A new double-scaling limit of \({\fancyscript{N}=4}\) super Yang-Mills theory and PP-wave strings. Nucl. Phys. B 643, 3 (2002). doi:10.1016/S0550-3213(02)00749-6 (arXiv:hep-th/0205033)

    MathSciNet  ADS  MATH  Google Scholar 

  63. Chu C.-S., Khoze V.V., Travaglini G.: Three-point functions in \({\fancyscript{N}=4}\) Yang-Mills theory and pp- waves. JHEP 0206, 011 (2002). doi:10.1088/1126-6708/2002/06/011 (arXiv:hep-th/0206005)

    MathSciNet  ADS  Google Scholar 

  64. Alday L.F., David J.R., Gava E., Narain K.S.: Structure constants of planar \({\fancyscript{N}=4}\) Yang Mills at one loop. JHEP 0509, 070 (2005). doi:10.1088/1126-6708/2005/09/070 (arXiv:hep-th/0502186)

    MathSciNet  ADS  Google Scholar 

  65. Georgiou G., Gili V.L., Russo R.: Operator mixing and the AdS/CFT correspondence. JHEP 0901, 082 (2009). doi:10.1088/1126-6708/2009/01/082 (arXiv:0810.0499)

    MathSciNet  ADS  Google Scholar 

  66. Georgiou G., Gili V.L., Russo R.: Operator mixing and three-point functions in \({\fancyscript{N}=4}\) SYM. JHEP 0910, 009 (2009). doi:10.1088/1126-6708/2009/10/009 (arXiv:0907.1567)

    MathSciNet  ADS  Google Scholar 

  67. Okuyama K., Tseng L.-S.: Three-point functions in \({\fancyscript{N}=4}\) SYM theory at one-loop. JHEP 0408, 055 (2004). doi:10.1088/1126-6708/2004/08/055 (arXiv:hep-th/0404190)

    MathSciNet  ADS  Google Scholar 

  68. Roiban R., Volovich A.: Yang-Mills correlation functions from integrable spin chains. JHEP 0409, 032 (2004). doi:10.1088/1126-6708/2004/09/032 (arXiv:hep-th/0407140)

    MathSciNet  ADS  Google Scholar 

  69. Escobedo, J., Gromov, N., Sever, A., Vieira, P.: Tailoring three-point functions and integrability. arXiv:1012.2475

  70. Grossardt, A., Plefka, J.: One-loop spectroscopy of scalar three-point functions in planar N = 4 super Yang-Mills theory. arXiv:1007.2356

  71. Dobashi S., Yoneya T.: Resolving the holography in the plane-wave limit of AdS/CFT correspondence. Nucl. Phys. B 711, 3 (2005). doi:10.1016/j.nuclphysb.2005.01.024 (arXiv:hep-th/0406225)

    MathSciNet  ADS  MATH  Google Scholar 

  72. Dobashi S., Yoneya T.: Impurity non-preserving 3-point correlators of BMN operators from pp-wave holography. I: Bosonic excitations. Nucl. Phys. B 711, 54 (2005). doi:10.1016/j.nuclphysb.2004.12.013 (arXiv:hep-th/0409058)

    MathSciNet  ADS  MATH  Google Scholar 

  73. Janik R.A., Surowka P., Wereszczynski A.: On correlation functions of operators dual to classical spinning string states. JHEP 1005, 030 (2010). doi:10.1007/JHEP05(2010)030 (arXiv:1002.4613)

    MathSciNet  ADS  Google Scholar 

  74. Dobashi S., Shimada H., Yoneya T.: Holographic reformulation of string theory on AdS 5 × S 5 background in the PP-wave limit. Nucl. Phys. B 665, 94 (2003). doi:10.1016/S0550-3213(03)00460-7 (arXiv:hep-th/0209251)

    MathSciNet  ADS  MATH  Google Scholar 

  75. Yoneya T.: Holography in the large J limit of AdS/CFT correspondence and its applications. Prog. Theor. Phys. Suppl. 164, 82 (2007). doi:10.1143/PTPS.164.82 (arXiv:hep-th/0607046)

    MathSciNet  ADS  Google Scholar 

  76. Tsuji A.: Holography of Wilson loop correlator and spinning strings. Prog. Theor. Phys. 117, 557 (2007). doi:10.1143/PTP.117.557 (arXiv:hep-th/0606030)

    MathSciNet  ADS  MATH  Google Scholar 

  77. Buchbinder E.I., Tseytlin A.A.: On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT. JHEP 1008, 057 (2010). doi:10.1007/JHEP08(2010)057 (arXiv:1005.4516)

    MathSciNet  ADS  Google Scholar 

  78. Tseytlin A.A.: On semiclassical approximation and spinning string vertex operators in AdS 5 × S 5. Nucl. Phys. B 664, 247 (2003). doi:10.1016/S0550-3213(03)00456-5 (arXiv:hep-th/0304139)

    MathSciNet  ADS  MATH  Google Scholar 

  79. Buchbinder E.I.: Energy-spin trajectories in AdS 5 × S 5 from semiclassical vertex operators. JHEP 1004, 107 (2010). doi:10.1007/JHEP04(2010)107 (arXiv:1002.1716)

    MathSciNet  ADS  Google Scholar 

  80. Zarembo K.: Holographic three-point functions of semiclassical states. JHEP 1009, 030 (2010). doi:10.1007/JHEP09(2010)030 (arXiv:1008.1059)

    MathSciNet  ADS  Google Scholar 

  81. Costa M.S., Monteiro R., Santos J.E., Zoakos D.: On three-point correlation functions in the gauge/gravity duality. JHEP 1011, 141 (2010). doi:10.1007/JHEP11(2010)141 (arXiv:1008.1070)

    MathSciNet  ADS  Google Scholar 

  82. Hernandez, R.: Three-point correlation functions from semiclassical circular strings. arXiv:1011.0408

  83. Ryang, S.: Correlators of vertex operators for circular strings with winding numbers in AdS 5 × S 5. arXiv:1011.3573

  84. Georgiou, G.: Two and three-point correlators of operators dual to folded string solutions at strong coupling. arXiv:1011.5181

  85. Roiban, R., Tseytlin, A.A.: On semiclassical computation of 3-point functions of closed string vertex operators in AdS 5 × S 5. arXiv:1008.4921

  86. Russo, J.G., Tseytlin A.A.: Large spin expansion of semiclassical 3-point correlators in AdS 5 × S 5. arXiv:1012.2760

  87. Polyakov A.M.: String theory and quark confinement. Nucl. Phys. Proc. Suppl. 68, 1 (1998). doi:10.1016/S0920-5632(98)00135-2 (arXiv:hep-th/9711002)

    MathSciNet  ADS  MATH  Google Scholar 

  88. Maldacena J.M.: Wilson loops in large N field theories. Phys. Rev. Lett. 80, 4859 (1998). doi:10.1103/PhysRevLett.80.4859 (arXiv:hep-th/9803002)

    MathSciNet  ADS  MATH  Google Scholar 

  89. Erickson J.K., Semenoff G.W., Zarembo K.: Wilson loops in \({\fancyscript{N}=4}\) supersymmetric Yang-Mills theory. Nucl. Phys. B 582, 155 (2000). doi:10.1016/S0550-3213(00)00300-X (arXiv:hep-th/0003055)

    MathSciNet  ADS  MATH  Google Scholar 

  90. Drukker N., Gross D.J.: An exact prediction of \({\fancyscript{N}=4}\) SUSYM theory for string theory. J. Math. Phys. 42, 2896 (2001). doi:10.1063/1.1372177 (hep-th/0010274)

    MathSciNet  ADS  MATH  Google Scholar 

  91. Bianchi, M., Green, M.B., Kovacs, S.: Instantons and BPS Wilson loops. arXiv:hep-th/0107028

  92. Bianchi M., Green M.B., Kovacs S.: Instanton corrections to circular Wilson loops in \({\fancyscript{N}=4}\) supersymmetric Yang-Mills. JHEP 0204, 040 (2002). doi:10.1088/1126-6708/2002/04/040 (arXiv:hep-th/0202003)

    MathSciNet  ADS  Google Scholar 

  93. Pestun, V.: Localization of gauge theory on a four-sphere and supersymmetric Wilson loops. arXiv:0712.2824

  94. Berenstein D.E., Corrado R., Fischler W., Maldacena J.M.: The operator product expansion for Wilson loops and surfaces in the large N limit. Phys. Rev. D 59, 105023 (1999). doi:10.1103/PhysRevD.59.105023 (arXiv:hep-th/9809188)

    MathSciNet  ADS  Google Scholar 

  95. Drukker N., Gross D.J., Ooguri H.: Wilson loops and minimal surfaces. Phys. Rev. D 60, 125006 (1999). doi:10.1103/PhysRevD.60.125006 (arXiv:hep-th/9904191)

    MathSciNet  ADS  Google Scholar 

  96. Drukker N., Gross D.J., Tseytlin A.A.: Green-Schwarz string in AdS 5 × S 5: Semiclassical partition function. JHEP 0004, 021 (2000). doi:10.1088/1126-6708/2000/04/021 (arXiv:hep-th/0001204)

    MathSciNet  ADS  Google Scholar 

  97. Kruczenski M., Tirziu A.: Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling. JHEP 0805, 064 (2008). doi:10.1088/1126-6708/2008/05/064 (arXiv:0803.0315)

    MathSciNet  Google Scholar 

  98. Zarembo K.: Supersymmetric Wilson loops. Nucl. Phys. B 643, 157 (2002). doi:10.1016/S0550-3213(02)00693-4 (arXiv:hep-th/0205160)

    MathSciNet  ADS  MATH  Google Scholar 

  99. Guralnik Z., Kulik B.: Properties of chiral Wilson loops. JHEP 0401, 065 (2004). doi:10.1088/1126-6708/2004/01/065 (arXiv:hep-th/0309118)

    MathSciNet  ADS  Google Scholar 

  100. Dymarsky A., Gubser S.S., Guralnik Z., Maldacena J.M.: Calibrated surfaces and supersymmetric Wilson loops. JHEP 0609, 057 (2006). doi:10.1088/1126-6708/2006/09/057 (arXiv:hep-th/0604058)

    MathSciNet  ADS  Google Scholar 

  101. Kapustin, A., Witten, E.: Electric-magnetic duality and the geometric Langlands program. arXiv:hep-th/0604151

  102. Drukker N.: 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model. JHEP 0609, 004 (2006). doi:10.1088/1126-6708/2006/09/004 (arXiv:hep-th/0605151)

    MathSciNet  ADS  Google Scholar 

  103. Drukker N., Giombi S., Ricci R., Trancanelli D.: More supersymmetric Wilson loops. Phys. Rev. D 76, 107703 (2007). doi:10.1103/PhysRevD.76.107703 (arXiv:0704. 2237)

    MathSciNet  ADS  Google Scholar 

  104. Drukker N., Giombi S., Ricci R., Trancanelli D.: Wilson loops: from four-dimensional SYM to two-dimensional YM. Phys. Rev. D 77, 047901 (2008). doi:10.1103/PhysRevD.77.047901 (arXiv:0707.2699)

    MathSciNet  ADS  Google Scholar 

  105. Drukker N., Giombi S., Ricci R., Trancanelli D.: Supersymmetric Wilson loops on S 3. JHEP 0805, 017 (2008). doi:10.1088/1126-6708/2008/05/017 (arXiv:0711.3226)

    MathSciNet  ADS  Google Scholar 

  106. Bassetto A., Griguolo L., Pucci F., Seminara D.: Supersymmetric Wilson loops at two loops. JHEP 0806, 083 (2008). doi:10.1088/1126-6708/2008/06/083 (arXiv: 0804.3973)

    MathSciNet  ADS  Google Scholar 

  107. Young D.: BPS Wilson loops on S 2 at higher loops. JHEP 0805, 077 (2008). doi:10.1088/1126-6708/2008/05/077 (arXiv:0804.4098)

    ADS  Google Scholar 

  108. Giombi S., Pestun V., Ricci R.: Notes on supersymmetric Wilson loops on a two-sphere. JHEP 1007, 088 (2010). doi:10.1007/JHEP07(2010)088 (arXiv:0905.0665)

    MathSciNet  ADS  Google Scholar 

  109. Pestun, V.: Localization of the four-dimensional N = 4 SYM to a two-sphere and 1/8 BPS Wilson loops. arXiv:0906.0638

  110. Dymarsky A., Pestun V.: Supersymmetric Wilson loops in N = 4 SYM and pure spinors. JHEP 1004, 115 (2010). doi:10.1007/JHEP04(2010)115 (arXiv:0911.1841)

    MathSciNet  ADS  Google Scholar 

  111. Drukker N., Trancanelli D.: A supermatrix model for \({\fancyscript{N}=6}\) super Chern-Simons -matter theory. JHEP 1002, 058 (2010). doi:10.1007/JHEP02(2010)058 (arXiv:0912. 3006)

    MathSciNet  ADS  Google Scholar 

  112. Kapustin A., Willett B., Yaakov I.: Exact results for Wilson loops in superconformal Chern-Simons theories with matter. JHEP 1003, 089 (2010). doi:10.1007/JHEP03(2010)089 (arXiv:0909.4559)

    MathSciNet  ADS  Google Scholar 

  113. Drukker N., Plefka J., Young D.: Wilson loops in 3-dimensional \({\fancyscript{N}=6}\) supersymmetric Chern-Simons theory and their string theory duals. JHEP 0811, 019 (2008). doi:10.1088/1126-6708/2008/11/019 (arXiv:0809.2787)

    MathSciNet  ADS  Google Scholar 

  114. Chen B., Wu J.-B.: Supersymmetric Wilson loops in \({\fancyscript{N}=6}\) super Chern-Simons-matter theory. Nucl. Phys. B 825, 38 (2010). doi:10.1016/j.nuclphysb.2009.09.015 (arXiv:0809.2863)

    ADS  MATH  Google Scholar 

  115. Rey S.-J., Suyama T., Yamaguchi S.: Wilson loops in superconformal Chern-Simons theory and fundamental strings in Anti-de Sitter supergravity dual. JHEP 0903, 127 (2009). doi:10.1088/1126-6708/2009/03/127 (arXiv:0809.3786)

    MathSciNet  ADS  Google Scholar 

  116. Marino M., Putrov P.: Exact results in ABJM theory from topological strings. JHEP 1006, 011 (2010). doi:10.1007/JHEP06(2010)011 (arXiv:0912.3074)

    MathSciNet  ADS  Google Scholar 

  117. Callan C.G., Maldacena J.M.: Brane dynamics from the Born-Infeld action. Nucl. Phys. B 513, 198 (1998). doi:10.1016/S0550-3213(97)00700-1 (arXiv:hep-th/9708147)

    MathSciNet  ADS  MATH  Google Scholar 

  118. Rey S.-J., Yee J.-T.: Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity. Eur. Phys. J. C 22, 379 (2001). doi:10.1007/s100520100799 (arXiv:hep-th/9803001)

    MathSciNet  ADS  MATH  Google Scholar 

  119. Drukker N., Fiol B.: All-genus calculation of Wilson loops using D-branes. JHEP 0502, 010 (2005). doi:10.1088/1126-6708/2005/02/010 (arXiv:hep-th/0501109)

    MathSciNet  ADS  Google Scholar 

  120. Gomis J., Passerini F.: Holographic Wilson loops. JHEP 0608, 074 (2006). doi:10.1088/1126-6708/2006/08/074 (arXiv:hep-th/0604007)

    MathSciNet  ADS  Google Scholar 

  121. Freyhult, L.: Review of AdS/CFT integrability, Chapter III.4: twist states and the cusp anomalous dimension. Lett. Math. Phys. Published in this volume. arXiv:1012. 3993

  122. Armoni A.: Anomalous dimensions from a spinning D5-brane. JHEP 0611, 009 (2006). doi:10.1088/1126-6708/2006/11/009 (arXiv:hep-th/0608026)

    MathSciNet  ADS  Google Scholar 

  123. Gang D., Park J.-S., Yamaguchi S.: Operator with large spin and spinning D3-brane. JHEP 0911, 024 (2009). doi:10.1088/1126-6708/2009/11/024 (arXiv:0908.3938)

    ADS  Google Scholar 

  124. Hartnoll S.A., Kumar S.P.: Higher rank Wilson loops from a matrix model. JHEP 0608, 026 (2006). doi:10.1088/1126-6708/2006/08/026 (arXiv:hep-th/0605027)

    MathSciNet  ADS  Google Scholar 

  125. Yamaguchi S.: Wilson loops of anti-symmetric representation and D5-branes. JHEP 0605, 037 (2006). doi:10.1088/1126-6708/2006/05/037 (arXiv:hep-th/0603208)

    ADS  Google Scholar 

  126. Okuyama K., Semenoff G.W.: Wilson loops in \({\fancyscript{N}=4}\) SYM and fermion droplets. JHEP 0606, 057 (2006). doi:10.1088/1126-6708/2006/06/057 (arXiv:hep-th/0604209)

    MathSciNet  ADS  Google Scholar 

  127. Lin H., Lunin O., Maldacena J.M.: Bubbling AdS space and 1/2 BPS geometries. JHEP 0410, 025 (2004). doi:10.1088/1126-6708/2004/10/025 (arXiv:hep-th/0409174)

    MathSciNet  ADS  Google Scholar 

  128. Yamaguchi S.: Bubbling geometries for half BPS Wilson lines. Int. J. Mod. Phys. A 22, 1353 (2007). doi:10.1142/S0217751X07035070 (arXiv:hep-th/0601089)

    ADS  MATH  Google Scholar 

  129. Lunin O.: On gravitational description of Wilson lines. JHEP 0606, 026 (2006). doi:10.1088/1126-6708/2006/06/026 (arXiv:hep-th/0604133)

    MathSciNet  ADS  Google Scholar 

  130. D’Hoker E., Estes J., Gutperle M.: Gravity duals of half-BPS Wilson loops. JHEP 0706, 063 (2007). doi:10.1088/1126-6708/2007/06/063 (arXiv:0705.1004)

    MathSciNet  Google Scholar 

  131. Okuda T.: A prediction for bubbling geometries. JHEP 0801, 003 (2008). doi:10.1088/1126-6708/2008/01/003 (arXiv:0708.3393)

    MathSciNet  ADS  Google Scholar 

  132. Okuda T., Trancanelli D.: Spectral curves, emergent geometry, and bubbling solutions for Wilson loops. JHEP 0809, 050 (2008). doi:10.1088/1126-6708/2008/09/050 (arXiv:0806.4191)

    MathSciNet  ADS  Google Scholar 

  133. Drukker N., Giombi S., Ricci R., Trancanelli D.: On the D3-brane description of some 1/4 BPS Wilson loops. JHEP 0704, 008 (2007). doi:10.1088/1126-6708/2007/04/008 (arXiv:hep-th/0612168)

    MathSciNet  ADS  Google Scholar 

  134. Drukker, N., Fiol, B.: On the integrability of Wilson loops in AdS 5 × S 5: Some periodic ansatze. JHEP 0601, 056 (2006) hep-th/0506058. doi:10.1088/1126-6708/2006/01/056

  135. Alday L.F., Maldacena J.M.: Gluon scattering amplitudes at strong coupling. JHEP 0706, 064 (2007). doi:10.1088/1126-6708/2007/06/064 (arXiv:0705.0303)

    MathSciNet  ADS  Google Scholar 

  136. Drukker N., Kawamoto S.: Small deformations of supersymmetric Wilson loops and open spin-chains. JHEP 0607, 024 (2006). doi:10.1088/1126-6708/2006/07/024 (arXiv:hep-th/0604124)

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Charlotte Kristjansen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kristjansen, C. Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity. Lett Math Phys 99, 349–374 (2012). https://doi.org/10.1007/s11005-011-0514-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-011-0514-9

Mathematics Subject Classification (2010)

Keywords

Navigation