Skip to main content

D5-brane boundary reflection factors


We compute the strong coupling limit of the boundary reflection factor for excitations on open strings attached to various kinds of D5-branes that probe AdS5×S5. We study the crossing equation, which constrains the boundary reflection factor, and propose that some solutions will give the boundary reflection factors for all values of the coupling. Our proposal passes various checks in the strong coupling limit by comparison with diverse explicit string theory computations. In some of the cases we consider, the D5-branes correspond to \( \frac{1}{2}-\mathrm{BPS} \) Wilson loops in the k-th rank antisymmetric representation of the dual field theory. In the other cases they correspond in the dual field theory to the addition of a fundamental hypermultiplet in a defect.

This is a preview of subscription content, access via your institution.


  1. [1]

    N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012)3 [arXiv:1012.3982] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  2. [2]

    N. Mann and S.E. Vazquez, Classical Open String Integrability, JHEP 04 (2007) 065 [hep-th/0612038] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  3. [3]

    A. Dekel and Y. Oz, Integrability of Green-Schwarz σ-models with Boundaries, JHEP 08 (2011)004 [arXiv:1106.3446] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  4. [4]

    D.M. Hofman and J.M. Maldacena, Reflecting magnons, JHEP 11 (2007) 063 [arXiv:0708.2272] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  5. [5]

    D. Correa and C. Young, Reflecting magnons from D7 and D5 branes, J. Phys. A 41 (2008) 455401 [arXiv:0808.0452] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  6. [6]

    D.H. Correa, V. Regelskis and C.A. Young, Integrable achiral D5-brane reflections and asymptotic Bethe equations, J. Phys. A 44 (2011) 325403 [arXiv:1105.3707] [INSPIRE].

    MathSciNet  Google Scholar 

  7. [7]

    S. Yamaguchi, Wilson loops of anti-symmetric representation and D5-branes, JHEP 05 (2006)037 [hep-th/0603208] [INSPIRE].

    ADS  Article  Google Scholar 

  8. [8]

    C.G. Callan Jr., A. Guijosa and K.G. Savvidy, Baryons and string creation from the five-brane world volume action, Nucl. Phys. B 547 (1999) 127 [hep-th/9810092] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  9. [9]

    M. Chernicoff and A. Guijosa, Energy Loss of Gluons, Baryons and k-Quarks in an N = 4 SYM Plasma, JHEP 02 (2007) 084 [hep-th/0611155] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  10. [10]

    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].

    ADS  Article  Google Scholar 

  11. [11]

    N. Drukker, Integrable Wilson loops, arXiv:1203.1617 [INSPIRE].

  12. [12]

    O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. [13]

    D. Arean, A.V. Ramallo and D. Rodriguez-Gomez, Mesons and Higgs branch in defect theories, Phys. Lett. B 641 (2006) 393 [hep-th/0609010] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  14. [14]

    J. Pawelczyk and S.-J. Rey, Ramond-Ramond flux stabilization of D-branes, Phys. Lett. B 493 (2000)395 [hep-th/0007154] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. [15]

    J. Camino, A. Paredes and A. Ramallo, Stable wrapped branes, JHEP 05 (2001) 011 [hep-th/0104082] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  16. [16]

    A. Karch and L. Randall, Open and closed string interpretation of SUSY CFTs on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  17. [17]

    K. Skenderis and M. Taylor, Branes in AdS and p p wave space-times, JHEP 06 (2002) 025 [hep-th/0204054] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  18. [18]

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

    MathSciNet  ADS  Article  Google Scholar 

  19. [19]

    N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].

    MathSciNet  Google Scholar 

  20. [20]

    K. Pohlmeyer, Integrable Hamiltonian Systems and Interactions Through Quadratic Constraints, Commun. Math. Phys. 46 (1976) 207 [INSPIRE].

    MathSciNet  ADS  MATH  Article  Google Scholar 

  21. [21]

    M. Grigoriev and A.A. Tseytlin, Pohlmeyer reduction of AdS 5 × S 5 superstring σ-model, Nucl. Phys. B 800 (2008) 450 [arXiv:0711.0155] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  22. [22]

    S. Ghoshal and A.B. Zamolodchikov, Boundary S matrix and boundary state in two-dimensional integrable quantum field theory, Int. J. Mod. Phys. A 9 (1994) 3841 [Erratum ibid. A 9 (1994) 4353] [hep-th/9306002] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  23. [23]

    H. Saleur, S. Skorik and N. Warner, The boundary sine-Gordon theory: Classical and semiclassical analysis, Nucl. Phys. B 441 (1995) 421 [hep-th/9408004] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  24. [24]

    R. Jackiw and G. Woo, Semiclassical Scattering of Quantized Nonlinear Waves, Phys. Rev. D 12 (1975) 1643 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  25. [25]

    D.M. Hofman and J.M. Maldacena, Giant Magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].

    MathSciNet  Google Scholar 

  26. [26]

    N. Gromov and A. Sever, Analytic Solution of Bremsstrahlung TBA, JHEP 11 (2012) 075 [arXiv:1207.5489] [INSPIRE].

    ADS  Article  Google Scholar 

  27. [27]

    M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, Penrose limits and maximal supersymmetry, Class. Quant. Grav. 19 (2002) L87 [hep-th/0201081] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  28. [28]

    D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N =4 super Yang-Mills,JHEP 04(2002)013[hep-th/0202021][INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  29. [29]

    N. Beisert, R. Hernandez and E. Lopez, A crossing-symmetric phase for AdS 5 × S 5 strings, JHEP 11 (2006) 070 [hep-th/0609044] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  30. [30]

    N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].

    Article  Google Scholar 

  31. [31]

    G. Arutyunov and S. Frolov, The Dressing Factor and Crossing Equations, J. Phys. A 42 (2009)425401 [arXiv:0904.4575] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  32. [32]

    A. LeClair, G. Mussardo, H. Saleur and S. Skorik, Boundary energy and boundary states in integrable quantum field theories, Nucl. Phys. B 453 (1995) 581 [hep-th/9503227] [INSPIRE].

    MathSciNet  ADS  Article  Google Scholar 

  33. [33]

    Z. Bajnok, L. Palla and G. Takács, Finite size effects in quantum field theories with boundary from scattering data, Nucl. Phys. B 716 (2005) 519 [hep-th/0412192] [INSPIRE].

    ADS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Diego H. Correa.

Additional information

ArXiv ePrint: 1301.3412

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Correa, D.H., Massolo, F.I.S. D5-brane boundary reflection factors. J. High Energ. Phys. 2013, 95 (2013).

Download citation


  • Wilson
  • ’t Hooft and Polyakov loops
  • AdS-CFT Correspondence
  • Integrable Field Theories