Abstract
We show how to construct an algebraic curve for factorized string solution in the context of the AdS/CFT correspondence. We define factorized solutions to be solutions where the flat-connection becomes independent of one of the worldsheet variables by a similarity transformation with a matrix S satisfying S −1 dS = const. Using the factorization property we construct a well defined Lax operator and an associated algebraic curve. The construction procedure is local and does not require the introduction of a monodromy matrix. The procedure can be applied for string solutions with any boundary conditions. We study the properties of the curve and give several examples for the application of the procedure.
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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. 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].
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].
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 et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
V. Kazakov, A. Marshakov, J. Minahan and K. Zarembo, Classical/quantum integrability in AdS/CFT, JHEP 05 (2004) 024 [hep-th/0402207] [INSPIRE].
V. Kazakov and K. Zarembo, Classical/quantum integrability in non-compact sector of AdS/CFT, JHEP 10 (2004) 060 [hep-th/0410105] [INSPIRE].
N. Beisert, V. Kazakov and K. Sakai, Algebraic curve for the SO(6) sector of AdS/CFT, Commun. Math. Phys. 263 (2006) 611 [hep-th/0410253] [INSPIRE].
N. Beisert, V. 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].
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].
S. Ryang, Algebraic curves for long folded and circular winding strings in AdS 5 × S 5, JHEP 02 (2013) 107 [arXiv:1212.6109] [INSPIRE].
G. Arutyunov, J. Russo and A.A. Tseytlin, Spinning strings in AdS 5 × S 5 : new integrable system relations, Phys. Rev. D 69 (2004) 086009 [hep-th/0311004] [INSPIRE].
M. Kruczenski, A note on twist two operators in N = 4 SYM and Wilson loops in Minkowski signature, JHEP 12 (2002) 024 [hep-th/0210115] [INSPIRE].
J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].
S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and Anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].
S.-x. Chu, D. Hou and H.-c. Ren, The subleading term of the strong coupling expansion of the heavy-quark potential in a N = 4 super Yang-Mills vacuum, JHEP 08 (2009) 004 [arXiv:0905.1874] [INSPIRE].
R.A. Janik, P. Surowka and A. Wereszczynski, On correlation functions of operators dual to classical spinning string states, JHEP 05 (2010) 030 [arXiv:1002.4613] [INSPIRE].
S. Gubser, I. Klebanov and A.M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
L. F. Alday, G. Arutyunov and S. Frolov, Green-schwarz strings in tst-transformed backgrounds, JHEP 06 (2006) 018 [hep-th/0512253] [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].
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].
N. Berkovits, M. Bershadsky, T. Hauer, S. Zhukov and B. Zwiebach, Superstring theory on AdS 2 × S 2 as a coset supermanifold, Nucl. Phys. B 567 (2000) 61 [hep-th/9907200] [INSPIRE].
I. Adam, A. Dekel, L. Mazzucato and Y. Oz, Integrability of type II superstrings on Ramond-Ramond backgrounds in various dimensions, JHEP 06 (2007) 085 [hep-th/0702083] [INSPIRE].
K. Zarembo, Strings on semisymmetric superspaces, JHEP 05 (2010) 002 [arXiv:1003.0465] [INSPIRE].
N. Drukker and V. Forini, Generalized quark-antiquark potential at weak and strong coupling, JHEP 06 (2011) 131 [arXiv:1105.5144] [INSPIRE].
M. Kruczenski, R. Roiban, A. Tirziu and A.A. Tseytlin, Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS 5 × S 5, Nucl. Phys. B 791 (2008) 93 [arXiv:0707.4254] [INSPIRE].
R. Roiban and A.A. Tseytlin, Strong-coupling expansion of cusp anomaly from quantum superstring, JHEP 11 (2007) 016 [arXiv:0709.0681] [INSPIRE].
K. Zarembo, Open string fluctuations in AdS 5 × S 5 and operators with large R charge, Phys. Rev. D 66 (2002) 105021 [hep-th/0209095] [INSPIRE].
N. Dorey and B. Vicedo, On the dynamics of finite-gap solutions in classical string theory, JHEP 07 (2006) 014 [hep-th/0601194] [INSPIRE].
A. Dekel and Y. Oz, Integrability of Green-Schwarz σ-models with boundaries, JHEP 08 (2011) 004 [arXiv:1106.3446] [INSPIRE].
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ArXiv ePrint: 1302.0555
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Dekel, A. Algebraic curves for factorized string solutions. J. High Energ. Phys. 2013, 119 (2013). https://doi.org/10.1007/JHEP04(2013)119
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DOI: https://doi.org/10.1007/JHEP04(2013)119