Skip to main content
Log in

Achiral boundaries and the twisted Yangian of the D5-brane

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We consider integrable field theories with achiral boundary conditions and uncover the underlying achiral twisted Yangian algebra. This construction arises from old work on the bosonic principal chiral model on a half-line, but finds a modern realization as the hidden symmetry in the planar limit of the scattering of worldsheet excitations of the AdS/CFT light-cone superstring off a D5-brane.

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. N. Beisert et al., Review of AdS/CFT integrability: an overview, arXiv:1012.3982 [SPIRES].

  2. K. Zoubos, Review of AdS/CFT integrability, chapter IV.2: deformations, orbifolds and open boundaries, arXiv:1012.3998 [SPIRES].

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

    Article  ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  5. N. MacKay and V. Regelskis, On the reflection of magnon bound states, JHEP 08 (2010) 055 [arXiv:1006.4102] [SPIRES].

    Article  ADS  Google Scholar 

  6. Z. Bajnok and L. Palla, Boundary finite size corrections for multiparticle states and planar AdS/CFT, JHEP 01 (2011) 011 [arXiv:1010.5617] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  7. A. Ciavarella, Giant magnons and non-maximal giant gravitons, JHEP 01 (2011) 040 [arXiv:1011.1440] [SPIRES].

    Article  ADS  Google Scholar 

  8. C. Ahn and R.I. Nepomechie, Yangian symmetry and bound states in AdS/CFT boundary scattering, JHEP 05 (2010) 016 [arXiv:1003.3361] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  9. N. MacKay and V. Regelskis, Yangian symmetry of the Y = 0 maximal giant graviton, JHEP 12 (2010) 076 [arXiv:1010.3761] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  10. L. Palla, Yangian symmetry of boundary scattering in AdS/CFT and the explicit form of bound state reflection matrices, JHEP 03 (2011) 110 [arXiv:1102.0122] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  11. G.W. Delius, N.J. MacKay and B.J. Short, Boundary remnant of Yangian symmetry and the structure of rational reflection matrices, Phys. Lett. B 522 (2001) 335 [hep-th/0109115] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  12. N. Beisert, The S-matrix of AdS/CFT and Yangian symmetry, PoS(Solvay)002 [arXiv:0704.0400] [SPIRES].

  13. A. Torrielli, Review of AdS/CFT integrability, chapter VI.2: Yangian algebra, arXiv:1012.4005 [SPIRES].

  14. A. Torrielli, Yangians, S-matrices and AdS/CFT, J. Phys. A 44 (2011) 263001 [arXiv:1104.2474] [SPIRES].

    ADS  Google Scholar 

  15. N.J. MacKay and B.J. Short, Boundary scattering, symmetric spaces and the principal chiral model on the half-line, Commun. Math. Phys. 233 (2003) 313 [hep-th/0104212] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  17. N.J. MacKay, Rational K-matrices and representations of twisted Yangians, J. Phys. A 35 (2002) 7865 [math.QA/0205155] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  18. J.P. Antoine and B. Piette, Classical non-linear σ-models on Grassmann manifolds of compact or non-compact type, J. Math. Phys. 28 (1987) 2753 [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. G.I. Olshanskii, Twisted Yangians and infinite-dimensional classical Lie algebras, Lect. Notes Math. 1510 (1992) 104.

    Article  MathSciNet  Google Scholar 

  20. A.I. Molev and E. Ragoucy, Representations of reflection algebras, Rev. Math. Phys. 14 (2002) 317 [math.QA/0107213].

    Article  MATH  MathSciNet  Google Scholar 

  21. A. Doikou, Quantum spin chain with ‘soliton non-preserving’ boundary conditions, J. Phys. A 33 (2000) 8797 [hep-th/0006197] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  22. N.J. MacKay and C.A.S. Young, Classically integrable boundary conditions for symmetric-space σ-models, Phys. Lett. B 588 (2004) 221 [hep-th/0402182] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  23. E. Ogievetsky, P. Wiegmann and N. Reshetikhin, The principal chiral field in two-dimensions on classical Lie algebras: the Bethe ansatz solution and factorized theory of scattering, Nucl. Phys. B 280 (1987) 45 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  24. 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 [hep-th/9306002] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  25. N.J. MacKay, Rational R-matrices in irreducible representations, J. Phys. A 24 (1991) 4017 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  26. I.V. Cherednik, Factorizing particles on a half line and root systems, T heor. Math. Phys. 61 (1984) 977 [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

  27. E.K. Sklyanin, Boundary conditions for integrable quantum systems, J. Phys. A 21 (1988) 2375 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  28. L. Mezincescu, R.I. Nepomechie and V. Rittenberg, Bethe ansatz solution of the Fateev-Zamolodchikov quantum spin chain with boundary terms, Phys. Lett. A 147 (1990) 70 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  29. L. Mezincescu and R.I. Nepomechie, Fusion procedure for open chains, J. Phys. A 25 (1992) 2533 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  30. N. Beisert, T he SU(2–2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [SPIRES].

    MathSciNet  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  32. M. de Leeuw, Bound states, Yangian symmetry and classical r-matrix for the AdS 5 × S 5 superstring, JHEP 06 (2008) 085 [arXiv:0804.1047] [SPIRES].

    Article  Google Scholar 

  33. G. Arutyunov, M. de Leeuw and A. Torrielli, The bound state S-matrix for AdS 5 × S 5 superstring, Nucl. Phys. B 819 (2009) 319 [arXiv:0902.0183] [SPIRES].

    Article  ADS  Google Scholar 

  34. G. Arutyunov and S. Frolov, The S-matrix of string bound states, Nucl. Phys. B 804 (2008) 90 [arXiv:0803.4323] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  35. H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  36. N.J. MacKay, Introduction to Yangian symmetry in integrable field theory, Int. J. Mod. Phys. A 20 (2005) 7189 [hep-th/0409183] [SPIRES].

    ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vidas Regelskis.

Additional information

ArXiv ePrint: 1105.4128

Rights and permissions

Reprints and permissions

About this article

Cite this article

MacKay, N., Regelskis, V. Achiral boundaries and the twisted Yangian of the D5-brane. J. High Energ. Phys. 2011, 19 (2011). https://doi.org/10.1007/JHEP08(2011)019

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP08(2011)019

Keywords

Navigation