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Yangian symmetry of the Y=0 maximal giant graviton

Journal of High Energy Physics volume 2010, Article number: 76 (2010) Cite this article

Abstract

We study the remnants of Yangian symmetry of AdS/CFT magnons reflecting from boundaries with no degrees of freedom. We present the generalized twisted boundary Yangian of open strings ending on boundaries which preserve only a subalgebra \( \mathfrak{h} \) of the bulk algebra \( \mathfrak{g} \), where \( \left( {\mathfrak{g},\mathfrak{h}} \right) \) is a symmetric pair. This is realized by open strings ending on the D3 brane known as the Y = 0 maximal giant graviton in AdS 5 × S 5. We also consider the Yangian symmetry of the boundary which preserves an \( \mathfrak{s}\mathfrak{u}\left( {\left. 1 \right|2} \right) \) subalgebra only.

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References

  1. J.A. Minahan and K. Zarembo, The Bethe-ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  2. I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  3. L. Dolan, C.R. Nappi and E. Witten, Yangian symmetry in D = 4 superconformal Yang-Mills theory, hep-th/0401243 [SPIRES].

  4. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].

    MATH  ADS  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  6. G. Arutyunov and S. Frolov, Foundations of the AdS 5 × S 5 superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  7. M. Staudacher, The factorized S-matrix of CFT/AdS, JHEP 05 (2005) 054 [hep-th/0412188] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  8. N. Beisert, The analytic bethe ansatz for a chain with centrally extended SU(2|2) symmetry, J. Stat. Mech. (2007) P01017 [nlin.SI/0610017].

  9. N. Dorey, Magnon bound states and the AdS/CFT correspondence, J. Phys. A 39 (2006) 13119 [hep-th/0604175] [SPIRES].

    MathSciNet  Google Scholar 

  10. H.-Y. Chen, N. Dorey and K. Okamura, The asymptotic spectrum of the N = 4 super Yang-Mills spin chain, JHEP 03 (2007) 005 [hep-th/0610295] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  11. 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 

  12. N. Beisert, The S-matrix of AdS/CFT and Yangian symmetry, PoS SOLVAY (2006) 002 [arXiv:0704.0400] [SPIRES].

  13. B.I. Zwiebel, Yangian symmetry at two-loops for the SU(2|1) sector of N = 4 SYM, J. Phys. A 40 (2007) 1141 [hep-th/0610283] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  14. V. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Sov. Math. Dokl. 32 (1985) 254.

    Google Scholar 

  15. D. Bernard, 2, An introduction to Yangian symmetries, Int. J. Mod. Phys. B 7 (1993) 3517 [hep-th/9211133] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  16. D. Arnaudon, A. Molev and E. Ragoucy, On the R-matrix realization of Yangians and their representations, Annales Henri Poincare 7 (2006) 1269 [math.QA/0511481v1].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. 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 

  18. 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 

  19. 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 

  20. 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 

  21. 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 

  22. A. Doikou, On boundary super algebras, J. Math. Phys. 51 (2010) 043509 [arXiv:0910.1203] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  23. A.I. Molev, Yangians and their applications, in Handbook of Algebra, volume 3, J.M. Lemm ed., North Holland, The Netherlands (2003) [math.QA/0211288].

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  25. T. Matsumoto and S. Moriyama, An exceptional algebraic origin of the AdS/CFT Yangian symmetry, JHEP 04 (2008) 022 [arXiv:0803.1212] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  26. F. Spill and A. Torrielli, On Drinfeld’s second realization of the AdS/CFT SU(2|2) Yangian, J. Geom. Phys. 59 (2009) 489 [arXiv:0803.3194] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. 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 

  28. 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 

  29. R.I. Nepomechie and É. Ragoucy, Analytical Bethe ansatz for the open AdS/CFT SU(1|1) spin chain, JHEP 12 (2008) 025 [arXiv:0810.5015] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  30. T. Matsumoto, S. Moriyama and A. Torrielli, A secret symmetry of the AdS/CFT S-matrix, JHEP 09 (2007) 099 [arXiv:0708.1285] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of York, Heslington, York, Y O10 5DD, U.K.

    Niall MacKay & Vidas Regelskis

  2. Vilnius University Institute of Theoretical Physics and Astronomy, Goštauto 12, Vilnius, 01108, Lithuania

    Vidas Regelskis

Authors
  1. Niall MacKay
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  2. Vidas Regelskis
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Correspondence to Vidas Regelskis.

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ArXiv ePrint: 1010.3761

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MacKay, N., Regelskis, V. Yangian symmetry of the Y=0 maximal giant graviton. J. High Energ. Phys. 2010, 76 (2010). https://doi.org/10.1007/JHEP12(2010)076

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  • DOI: https://doi.org/10.1007/JHEP12(2010)076

Keywords

  • AdS-CFT Correspondence
  • Boundary Quantum Field Theory
  • Exact S-Matrix