Abstract
We consider the integrable open-chain transfer matrix corresponding to a Y = 0 brane at one boundary, and a Y θ = 0 brane (rotated with the respect to the former by an angle θ) at the other boundary. We determine the exact eigenvalues of this transfer matrix in terms of solutions of a corresponding set of Bethe equations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS 5 × S 5 background, Nucl. Phys. B 533 (1998) 109 [hep-th/9805028] [INSPIRE].
L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theories, Nucl. Phys. B 121 (1977) 77 [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
T. Klose, Review of AdS/CFT Integrability, Chapter IV.3: N = 6 Chern-Simons and Strings on AdS 4 × CP 3, Lett. Math. Phys. 99 (2012) 401 [arXiv:1012.3999] [INSPIRE].
A. Sfondrini, Towards integrability for AdS3 /CFT2, J. Phys. A 48 (2015) 023001 [arXiv:1406.2971] [INSPIRE].
N. Beisert, The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry, J. Stat. Mech. (2007) P01017, [nlin/0610017].
M.J. Martins and C.S. Melo, The Bethe ansatz approach for factorizable centrally extended S-matrices, Nucl. Phys. B 785 (2007) 246 [hep-th/0703086] [INSPIRE].
N. Beisert and M. Staudacher, Long-range PSU(2, 2|4) Bethe Ansatze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [INSPIRE].
D. Berenstein and S.E. Vazquez, Integrable open spin chains from giant gravitons, JHEP 06 (2005) 059 [hep-th/0501078] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Reflecting magnons, JHEP 11 (2007) 063 [arXiv:0708.2272] [INSPIRE].
W. Galleas, The Bethe Ansatz Equations for Reflecting Magnons, Nucl. Phys. B 820 (2009) 664 [arXiv:0902.1681] [INSPIRE].
Z. Bajnok and L. Palla, Boundary finite size corrections for multiparticle states and planar AdS/CFT, JHEP 01 (2011) 011 [arXiv:1010.5617] [INSPIRE].
Z. Bajnok, R.I. Nepomechie, L. Palla and R. Suzuki, Y-system for Y = 0 brane in planar AdS/CFT, JHEP 08 (2012) 149 [arXiv:1205.2060] [INSPIRE].
Z. Bajnok et al., The spectrum of tachyons in AdS/CFT, JHEP 03 (2014) 055 [arXiv:1312.3900] [INSPIRE].
K. Zoubos, Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries, Lett. Math. Phys. 99 (2012) 375 [arXiv:1012.3998] [INSPIRE].
M. Martins and P. Ramos, The Quantum Inverse Scattering Method for Hubbard-like Models, Nucl. Phys. B 522 (1998) 413 [solv-int/9712014].
X.-W. Guan, Algebraic Bethe ansatz for the one-dimensional Hubbard model with open boundaries, J. Phys. A 33 (2000) 5391 [cond-mat/9908054].
J. Cao, W.-L. Yang, K. Shi and Y. Wang, Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions, Nucl. Phys. B 875 (2013) 152 [arXiv:1306.1742] [INSPIRE].
Y. Wang, W.-L. Yang, J. Cao and K. Shi, Off-Diagonal Bethe Ansatz for Exactly Solvable Models, Springer, Heidelberg Germany (2015).
Y.-Y. Li, J. Cao, W.-L. Yang, K. Shi and Y. Wang, Exact solution of the one-dimensional Hubbard model with arbitrary boundary magnetic fields, Nucl. Phys. B 879 (2014) 98 [arXiv:1311.0432] [INSPIRE].
X. Zhang, J. Cao, W.-L. Yang, K. Shi and Y. Wang, Exact solution of the one-dimensional super-symmetric t-J model with unparallel boundary fields, J. Stat. Mech. (2014) P04031 [arXiv:1312.0376] [INSPIRE].
G. Arutyunov and S. Frolov, On String S-matrix, Bound States and TBA, JHEP 12 (2007) 024 [arXiv:0710.1568] [INSPIRE].
N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].
G. Arutyunov and S. Frolov, The S-matrix of String Bound States, Nucl. Phys. B 804 (2008) 90 [arXiv:0803.4323] [INSPIRE].
C. Ahn and R.I. Nepomechie, Yangian symmetry and bound states in AdS/CFT boundary scattering, JHEP 05 (2010) 016 [arXiv:1003.3361] [INSPIRE].
I.V. Cherednik, Factorizing Particles on a Half Line and Root Systems, Theor. Math. Phys. 61 (1984) 977 [INSPIRE].
E.K. Sklyanin, Boundary Conditions for Integrable Quantum Systems, J. Phys. A 21 (1988) 2375 [INSPIRE].
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].
A.J. Bracken, X.-Y. Ge, Y.-Z. Zhang and H.-Q. Zhou, Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons, Nucl. Phys. B 516 (1998) 588 [cond-mat/9710141].
R. Murgan and R.I. Nepomechie, Open-chain transfer matrices for AdS/CFT, JHEP 09 (2008) 085 [arXiv:0808.2629] [INSPIRE].
R.I. Nepomechie, An inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin, J. Phys. A 46 (2013) 442002 [arXiv:1307.5049] [INSPIRE].
J. Avan, S. Belliard, N. Grosjean and R.A. Pimenta, Modified algebraic Bethe ansatz for XXZ chain on the segment-III — Proof, arXiv:1506.02147.
N. Gromov, V. Kazakov and P. Vieira, Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 103(2009) 131601 [arXiv:0901.3753] [INSPIRE].
F.H.L. Essler, H. Frahm, F. Gohmann, A. Klumper and V.E. Korepin, The One-Dimensional Hubbard Model, Cambridge University Press, Cambridge U.K. (2005).
A. Prinsloo, V. Regelskis and A. Torrielli, Integrable open spin-chains in AdS3/CFT2, arXiv:1505.06767 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1507.08866
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Zhang, X., Cao, J., Cui, S. et al. Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries. J. High Energ. Phys. 2015, 133 (2015). https://doi.org/10.1007/JHEP10(2015)133
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2015)133