Abstract
For type II supergravity backgrounds with superisometries the corresponding transformations and conserved currents for the superstring are constructed up to fourth order in Θ. It is then shown how, for certain backgrounds related to near horizon geometries of intersecting branes, the components of the superisometry current can be used to construct a Lax connection demonstrating the classical integrability of the string in these backgrounds. This includes examples of AdS 2 and AdS 3 backgrounds with a D(2, 1; α) isometry group which have not previously been studied from an integrability point of view. The construction of the Lax connection is carried out up to second order in Θ.
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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].
J.A. Minahan and K. Zarembo, The Bethe ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [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, C. Ahn, L.F. Alday, Z. Bajnok, J.M. Drummond et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
G. Arutyunov and S. Frolov, Superstrings on AdS 4 × CP 3 as a Coset σ-model, JHEP 09 (2008) 129 [arXiv:0806.4940] [INSPIRE].
B. Stefanski Jr., Green-Schwarz action for Type IIA strings on AdS 4 × CP 3, Nucl. Phys. B 808 (2009) 80 [arXiv:0806.4948] [INSPIRE].
J. Gomis, D. Sorokin and L. Wulff, The Complete AdS 4 × CP 3 superspace for the type IIA superstring and D-branes, JHEP 03 (2009) 015 [arXiv:0811.1566] [INSPIRE].
P.A. Grassi, D. Sorokin and L. Wulff, Simplifying superstring and D-brane actions in AdS 4 × CP 3 superbackground, JHEP 08 (2009) 060 [arXiv:0903.5407] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
A. Babichenko, B. Stefanski Jr. and K. Zarembo, Integrability and the AdS 3 /CFT 2 correspondence, JHEP 03 (2010) 058 [arXiv:0912.1723] [INSPIRE].
A. Cagnazzo and K. Zarembo, B-field in AdS 3 /CFT 2 Correspondence and Integrability, JHEP 11 (2012) 133 [Erratum ibid. 1304 (2013) 003] [arXiv:1209.4049] [INSPIRE].
D. Bykov, The worldsheet low-energy limit of the AdS 4 × CP 3 superstring, Nucl. Phys. B 838 (2010) 47 [arXiv:1003.2199] [INSPIRE].
B. Basso and A. Rej, On the integrability of two-dimensional models with U(1) × SU(N) symmetry, Nucl. Phys. B 866 (2013) 337 [arXiv:1207.0413] [INSPIRE].
P. Sundin and L. Wulff, The low energy limit of the AdS 3 × S 3 × M 4 spinning string, JHEP 10 (2013) 111 [arXiv:1306.6918] [INSPIRE].
D. Sorokin and L. Wulff, Evidence for the classical integrability of the complete AdS 4 × CP 3 superstring, JHEP 11 (2010) 143 [arXiv:1009.3498] [INSPIRE].
P. Sundin and L. Wulff, Classical integrability and quantum aspects of the AdS 3 × S 3 × S 3 × S 1 superstring, JHEP 10 (2012) 109 [arXiv:1207.5531] [INSPIRE].
D. Sorokin, A. Tseytlin, L. Wulff and K. Zarembo, Superstrings in AdS 2 × S(2) × T(6), J. Phys. A 44 (2011) 275401 [arXiv:1104.1793] [INSPIRE].
A. Cagnazzo, D. Sorokin and L. Wulff, More on integrable structures of superstrings in AdS 4 × CP(3) and AdS 2 × S 2 × T(6) superbackgrounds, JHEP 01 (2012) 004 [arXiv:1111.4197] [INSPIRE].
H.J. Boonstra, B. Peeters and K. Skenderis, Brane intersections, anti-de Sitter space-times and dual superconformal theories, Nucl. Phys. B 533 (1998) 127 [hep-th/9803231] [INSPIRE].
G. Papadopoulos and P.K. Townsend, Intersecting M-branes, Phys. Lett. B 380 (1996) 273 [hep-th/9603087] [INSPIRE].
A.A. Tseytlin, Harmonic superpositions of M-branes, Nucl. Phys. B 475 (1996) 149 [hep-th/9604035] [INSPIRE].
J.P. Gauntlett, D.A. Kastor and J.H. Traschen, Overlapping branes in M-theory, Nucl. Phys. B 478 (1996) 544 [hep-th/9604179] [INSPIRE].
A.A. Tseytlin, ‘No force’ condition and BPS combinations of p-branes in eleven-dimensions and ten-dimensions, Nucl. Phys. B 487 (1997) 141 [hep-th/9609212] [INSPIRE].
K. Zarembo, Strings on Semisymmetric Superspaces, JHEP 05 (2010) 002 [arXiv:1003.0465] [INSPIRE].
K. Zarembo, Algebraic Curves for Integrable String Backgrounds, arXiv:1005.1342 [INSPIRE].
L. Wulff, The type-II superstring to order θ 4, JHEP 07 (2013) 123 [arXiv:1304.6422] [INSPIRE].
P. Claus and R. Kallosh, Superisometries of the AdS x S superspace, JHEP 03 (1999) 014 [hep-th/9812087] [INSPIRE].
M.J. Duff, H. Lü and C.N. Pope, AdS 5 × S 5 untwisted, Nucl. Phys. B 532 (1998) 181 [hep-th/9803061] [INSPIRE].
S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [INSPIRE].
B.E.W. Nilsson and C.N. Pope, Hopf Fibration of Eleven-dimensional Supergravity, Class. Quant. Grav. 1 (1984) 499 [INSPIRE].
D.P. Sorokin, V.I. Tkach and D.V. Volkov, On the relationship between compactified vacua OF D = 11 and D = 10 supergravities, Phys. Lett. B 161 (1985) 301 [INSPIRE].
P.M. Cowdall and P.K. Townsend, Gauged supergravity vacua from intersecting branes, Phys. Lett. B 429 (1998) 281 [Erratum ibid. B 434 (1998) 458] [hep-th/9801165] [INSPIRE].
J.P. Gauntlett, G.W. Gibbons, G. Papadopoulos and P.K. Townsend, Hyper-Kähler manifolds and multiply intersecting branes, Nucl. Phys. B 500 (1997) 133 [hep-th/9702202] [INSPIRE].
A. Stepanchuk and A.A. Tseytlin, On (non)integrability of classical strings in p-brane backgrounds, J. Phys. A 46 (2013) 125401 [arXiv:1211.3727] [INSPIRE].
Y. Chervonyi and O. Lunin, (Non)-Integrability of Geodesics in D-brane Backgrounds, JHEP 02 (2014) 061 [arXiv:1311.1521] [INSPIRE].
T. Lloyd and B. Stefanski, AdS 3 /CFT 2 , finite-gap equations and massless modes, arXiv:1312.3268 [INSPIRE].
P. Sundin and L. Wulff, Worldsheet scattering in AdS 3 /CFT 2, JHEP 07 (2013) 007 [arXiv:1302.5349] [INSPIRE].
L. Bianchi, V. Forini and B. Hoare, Two-dimensional S-matrices from unitarity cuts, JHEP 07 (2013) 088 [arXiv:1304.1798] [INSPIRE].
B. Hoare and A.A. Tseytlin, Massive S-matrix of AdS 3 × S 3 × T 4 superstring theory with mixed 3-form flux, Nucl. Phys. B 873 (2013) 395 [arXiv:1304.4099] [INSPIRE].
O.T. Engelund, R.W. McKeown and R. Roiban, Generalized unitarity and the worldsheet S matrix in AdS n × S n × M 10−2n, JHEP 08 (2013) 023 [arXiv:1304.4281] [INSPIRE].
R. Borsato, O.O. Sax, A. Sfondrini, B. Stefanski Jr. and A. Torrielli, Dressing phases of AdS3/CFT2, Phys. Rev. D 88 (2013) 066004 [arXiv:1306.2512] [INSPIRE].
M.C. Abbott, J. Murugan, P. Sundin and L. Wulff, Scattering in AdS 2 /CFT 1 and the BES Phase, JHEP 10 (2013) 066 [arXiv:1308.1370] [INSPIRE].
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Wulff, L. Superisometries and integrability of superstrings. J. High Energ. Phys. 2014, 115 (2014). https://doi.org/10.1007/JHEP05(2014)115
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DOI: https://doi.org/10.1007/JHEP05(2014)115