Abstract
The concept of spectral curve is generalized to open strings in AdS/CFT with integrability preserving boundary conditions. Our definition is based on the logarithms of the eigenvalues of the open monodromy matrix and makes possible to determine all the analytic, symmetry and asymptotic properties of the quasimomenta. We work out the details of the whole construction for the Y = 0 brane boundary condition. The quasimomenta of open circular strings are explicitly calculated. We use the asymptotic solutions of the Y -system and the boundary Bethe Ansatz equations to recover the spectral curve in the strong coupling scaling limit. Using the curve the quasiclassical fluctuations of some open string solutions are also studied.
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References
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] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
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] [INSPIRE].
N. Beisert, V.A. Kazakov, K. Sakai and K. Zarembo, The algebraic curve of classical superstrings on AdS 5 × S 5, Commun. Math. Phys. 263 (2006) 659 [hep-th/0502226] [INSPIRE].
V.A. Kazakov, A. Marshakov, J.A. Minahan and K. Zarembo, Classical/quantum integrability in AdS/CFT, JHEP 05 (2004) 024 [hep-th/0402207] [INSPIRE].
N. Gromov and P. Vieira, The AdS 5 × S 5 superstring quantum spectrum from the algebraic curve, Nucl. Phys. B 789 (2008) 175 [hep-th/0703191] [INSPIRE].
N. Beisert and M. Staudacher, Long-range PSU(2, 2|4) Bethe ansätze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [INSPIRE].
P. Vieira, Integrability in AdS/CFT: Bethe ansatz and string quantization beyond infinite volume, Ph.D. thesis, U. Porto, Porto Portugal (2008).
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].
D. Bombardelli, D. Fioravanti and R. Tateo, Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal, J. Phys. A 42 (2009) 375401 [arXiv:0902.3930] [INSPIRE].
G. Arutyunov and S. Frolov, Thermodynamic Bethe ansatz for the AdS 5 × S 5 mirror model, JHEP 05 (2009) 068 [arXiv:0903.0141] [INSPIRE].
N. Gromov, Y-system and quasi-classical strings, JHEP 01 (2010) 112 [arXiv:0910.3608] [INSPIRE].
N. Gromov, V. Kazakov and Z. Tsuboi, PSU(2, 2|4) character of quasiclassical AdS/CFT, JHEP 07 (2010) 097 [arXiv:1002.3981] [INSPIRE].
D.M. Hofman and J.M. Maldacena, Reflecting magnons, JHEP 11 (2007) 063 [arXiv:0708.2272] [INSPIRE].
C. Ahn and R.I. Nepomechie, The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons, JHEP 05 (2008) 059 [arXiv:0804.4036] [INSPIRE].
N. Mann and S.E. Vazquez, Classical open string integrability, JHEP 04 (2007) 065 [hep-th/0612038] [INSPIRE].
A. Dekel and Y. Oz, Integrability of Green-Schwarz σ-models with boundaries, JHEP 08 (2011) 004 [arXiv:1106.3446] [INSPIRE].
G. Arutyunov and S. Frolov, Foundations of the AdS 5 × S 5 superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].
B. Stefanski Jr., Open spinning strings, JHEP 03 (2004) 057 [hep-th/0312091] [INSPIRE].
N. Gromov, Integrability in AdS/CFT correspondence: quasi-classical analysis, J. Phys. A 42 (2009) 254004 [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].
N. Gromov and V. Kazakov, Review of AdS/CFT integrability, chapter III.7: Hirota dynamics for quantum integrability, Lett. Math. Phys. 99 (2012) 321 [arXiv:1012.3996] [INSPIRE].
G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256] [INSPIRE].
N. Gromov, S. Schäfer-Nameki and P. Vieira, Efficient precision quantization in AdS/CFT, JHEP 12 (2008) 013 [arXiv:0807.4752] [INSPIRE].
W. Galleas, The Bethe ansatz equations for reflecting magnons, Nucl. Phys. B 820 (2009) 664 [arXiv:0902.1681] [INSPIRE].
R.I. Nepomechie, Bethe ansatz equations for open spin chains from giant gravitons, JHEP 05 (2009) 100 [arXiv:0903.1646] [INSPIRE].
V. Balasubramanian, M.-X. Huang, T.S. Levi and A. Naqvi, Open strings from N = 4 super Yang-Mills, JHEP 08 (2002) 037 [hep-th/0204196] [INSPIRE].
J.A. Minahan, A. Tirziu and A.A. Tseytlin, Infinite spin limit of semiclassical string states, JHEP 08 (2006) 049 [hep-th/0606145] [INSPIRE].
Y. Hatsuda and R. Suzuki, Finite-size effects for multi-magnon states, JHEP 09 (2008) 025 [arXiv:0807.0643] [INSPIRE].
C. Ahn, M. Kim and B.-H. Lee, Quantum finite-size effects for dyonic magnons in the AdS 4 × CP 3, JHEP 09 (2010) 062 [arXiv:1007.1598] [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].
N. Gromov, S. Schäfer-Nameki and P. Vieira, Quantum wrapped giant magnon, Phys. Rev. D 78 (2008) 026006 [arXiv:0801.3671] [INSPIRE].
G. Arutyunov, S. Frolov and M. Zamaklar, The Zamolodchikov-Faddeev algebra for AdS 5 × S 5 superstring, JHEP 04 (2007) 002 [hep-th/0612229] [INSPIRE].
D.H. Correa and F.I. Schaposnik Massolo, D5-brane boundary reflection factors, JHEP 05 (2013) 095 [arXiv:1301.3412] [INSPIRE].
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].
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] [INSPIRE].
D.H. Correa and C.A.S. Young, Asymptotic Bethe equations for open boundaries in planar AdS/CFT, J. Phys. A 43 (2010) 145401 [arXiv:0912.0627] [INSPIRE].
N. Drukker, Integrable Wilson loops, JHEP 10 (2013) 135 [arXiv:1203.1617] [INSPIRE].
R.A. Janik and P. Laskos-Grabowski, Surprises in the AdS algebraic curve constructions: Wilson loops and correlation functions, Nucl. Phys. B 861 (2012) 361 [arXiv:1203.4246] [INSPIRE].
A. Dekel, Algebraic curves for factorized string solutions, JHEP 04 (2013) 119 [arXiv:1302.0555] [INSPIRE].
A. Dekel and T. Klose, Correlation function of circular Wilson loops at strong coupling, JHEP 11 (2013) 117 [arXiv:1309.3203] [INSPIRE].
N. Gromov and A. Sever, Analytic solution of Bremsstrahlung TBA, JHEP 11 (2012) 075 [arXiv:1207.5489] [INSPIRE].
N. Gromov, F. Levkovich-Maslyuk and G. Sizov, Analytic solution of Bremsstrahlung TBA II: turning on the sphere angle, JHEP 10 (2013) 036 [arXiv:1305.1944] [INSPIRE].
G. Sizov and S. Valatka, Algebraic curve for a cusped Wilson line, arXiv:1306.2527 [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum spectral curve for AdS 5 /CFT 4, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
B. Chen, X.-J. Wang and Y.-S. Wu, Integrable open spin chain in super Yang-Mills and the plane wave/SYM duality, JHEP 02 (2004) 029 [hep-th/0401016] [INSPIRE].
B. Chen, X.-J. Wang and Y.-S. Wu, Open spin chain and open spinning string, Phys. Lett. B 591 (2004) 170 [hep-th/0403004] [INSPIRE].
K. Okamura, Y. Takayama and K. Yoshida, Open spinning strings and AdS/dCF T duality, JHEP 01 (2006) 112 [hep-th/0511139] [INSPIRE].
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Bajnok, Z., Kim, M. & Palla, L. Spectral curve for open strings attached to the Y = 0 brane. J. High Energ. Phys. 2014, 35 (2014). https://doi.org/10.1007/JHEP04(2014)035
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DOI: https://doi.org/10.1007/JHEP04(2014)035