Classical integrability and quantum aspects of the AdS\(_3\times S^3\times S^3\times S^1\) superstring. (English) Zbl 1397.81400
Summary: In this paper we continue the investigation of aspects of integrability of the type IIA \(\text{AdS}_3\times S^3\times S^3\times S^1\) and \(\text{AdS}_3\times S^3\times T^4\) superstrings. By constructing a one parameter family of flat connections we prove that the Green-Schwarz string is classically integrable, at least to quadratic order in fermions, without fixing the kappa-symmetry. We then compare the quantum dispersion relation, fixed by integrability up to an unknown interpolating function \(h(\lambda)\), to explicit one-loop calculations on the string worldsheet. For \(\text{AdS}_3\times S^3\times S^3\times S^1\) the spectrum contains heavy, as well as light and massless modes, and we find that the one-loop contribution differs depending on how we treat these modes showing that similar regularization ambiguities as appeared in \(\text{AdS}_4/\text{CFT}_3\) occur also here.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
Keywords:
superstrings and heterotic strings; AdS-CFT correspondence; Bethe ansatz; integrable field theoriesReferences:
| [1] | Babichenko, A.; Stefanski, B.; Zarembo, K., Integrability and the ads_{3}/CF T_{2} correspondence, JHEP, 03, 058, (2010) · Zbl 1271.81118 · doi:10.1007/JHEP03(2010)058 |
| [2] | Elitzur, S.; Feinerman, O.; Giveon, A.; Tsabar, D., String theory on ads_{3} × S\^{}{3} × S\^{}{3} × S\^{}{1}, Phys. Lett., B 449, 180, (1999) · Zbl 1058.81649 |
| [3] | Gauntlett, JP; Myers, RC; Townsend, P., Supersymmetry of rotating branes, Phys. Rev., D 59, 025001, (1999) |
| [4] | Cowdall, P.; Townsend, P., Gauged supergravity vacua from intersecting branes, Phys. Lett., B 429, 281, (1998) · Zbl 1355.83030 |
| [5] | Boonstra, HJ; Peeters, B.; Skenderis, K., Brane intersections, anti-de Sitter space-times and dual superconformal theories, Nucl. Phys., B 533, 127, (1998) · Zbl 0956.81060 · doi:10.1016/S0550-3213(98)00512-4 |
| [6] | Papadopoulos, G.; Russo, J.; Tseytlin, AA, Curved branes from string dualities, Class. Quant. Grav., 17, 1713, (2000) · Zbl 0983.83043 · doi:10.1088/0264-9381/17/7/310 |
| [7] | Giveon, A.; Pakman, A., More on superstrings in ads_{3} × N, JHEP, 03, 056, (2003) · doi:10.1088/1126-6708/2003/03/056 |
| [8] | Boer, J.; Pasquinucci, A.; Skenderis, K., AdS/CFT dualities involving large 2D N = 4 superconformal symmetry, Adv. Theor. Math. Phys., 3, 577, (1999) · Zbl 0989.81088 |
| [9] | David, JR; Sahoo, B., Giant magnons in the D1-D5 system, JHEP, 07, 033, (2008) · doi:10.1088/1126-6708/2008/07/033 |
| [10] | David, JR; Sahoo, B., S-matrix for magnons in the D1-D5 system, JHEP, 10, 112, (2010) · Zbl 1291.81239 · doi:10.1007/JHEP10(2010)112 |
| [11] | Maldacena, JM; Ooguri, H., Strings in ads_{3} and SL(2, R) WZW model 1. the spectrum, J. Math. Phys., 42, 2929, (2001) · Zbl 1036.81033 · doi:10.1063/1.1377273 |
| [12] | Maldacena, JM; Ooguri, H.; Son, J., Strings in ads_{3} and the SL(2, \( \mathbb{R} \)) WZW model. part 2. Euclidean black hole, J. Math. Phys., 42, 2961, (2001) · Zbl 1036.81034 · doi:10.1063/1.1377039 |
| [13] | Maldacena, JM; Ooguri, H., Strings in ads_{3} and the SL(2, \( \mathbb{R} \)) WZW model. part 3. correlation functions, Phys. Rev., D 65, 106006, (2002) |
| [14] | Gava, E.; Narain, K., Proving the PP wave/CFT(2) duality, JHEP, 12, 023, (2002) · doi:10.1088/1126-6708/2002/12/023 |
| [15] | Lunin, O.; Mathur, SD, Rotating deformations of ads_{3} × S\^{}{3}, the orbifold CFT and strings in the pp wave limit, Nucl. Phys., B 642, 91, (2002) · Zbl 0998.81100 · doi:10.1016/S0550-3213(02)00677-6 |
| [16] | Gomis, J.; Motl, L.; Strominger, A., Pp wave/CFT(2) duality, JHEP, 11, 016, (2002) · doi:10.1088/1126-6708/2002/11/016 |
| [17] | Sommovigo, L., Penrose limit of ads_{3} × S\^{}{3} × S\^{}{3} × S\^{}{1} and its associated σ-model, JHEP, 07, 035, (2003) · doi:10.1088/1126-6708/2003/07/035 |
| [18] | Sadri, D.; Sheikh-Jabbari, MM, String theory on parallelizable pp waves, JHEP, 06, 005, (2003) · doi:10.1088/1126-6708/2003/06/005 |
| [19] | Gukov, S.; Martinec, E.; Moore, GW; Strominger, A., The search for a holographic dual to ads_{3} × S\^{}{3} × S\^{}{3} × S\^{}{1}, Adv. Theor. Math. Phys., 9, 435, (2005) · Zbl 1121.81106 |
| [20] | Bena, I.; Polchinski, J.; Roiban, R., Hidden symmetries of the ads_{5} × S\^{}{5} superstring, Phys. Rev., D 69, 046002, (2004) |
| [21] | Kazakov, V.; Marshakov, A.; Minahan, J.; Zarembo, K., Classical/quantum integrability in AdS/CFT, JHEP, 05, 024, (2004) · doi:10.1088/1126-6708/2004/05/024 |
| [22] | Beisert, N.; Kazakov, V.; Sakai, K.; Zarembo, K., The algebraic curve of classical superstrings on ads_{5} × S\^{}{5}, Commun. Math. Phys., 263, 659, (2006) · Zbl 1125.81037 · doi:10.1007/s00220-006-1529-4 |
| [23] | Staudacher, M., The factorized S-matrix of CFT/AdS, JHEP, 05, 054, (2005) · doi:10.1088/1126-6708/2005/05/054 |
| [24] | Beisert, N., The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys., 12, 945, (2008) |
| [25] | Arutyunov, G.; Frolov, S., Superstrings on ads_{4} × CP\^{}{3} as a coset σ-model, JHEP, 09, 129, (2008) · Zbl 1245.81136 · doi:10.1088/1126-6708/2008/09/129 |
| [26] | Gomis, J.; Sorokin, D.; Wulff, L., The complete ads_{4} × CP\^{}{3} superspace for the type IIA superstring and D-branes, JHEP, 03, 015, (2009) · doi:10.1088/1126-6708/2009/03/015 |
| [27] | Rughoonauth, N.; Sundin, P.; Wulff, L., Near BMN dynamics of the ads_{3} × S\^{}{3} × S_{3} × S_{1} superstring, JHEP, 07, 159, (2012) · Zbl 1397.81282 · doi:10.1007/JHEP07(2012)159 |
| [28] | Grassi, PA; Sorokin, D.; Wulff, L., Simplifying superstring and D-brane actions in ads_{4} × CP \^{}{3} superbackground, JHEP, 08, 060, (2009) · doi:10.1088/1126-6708/2009/08/060 |
| [29] | Cagnazzo, A.; Sorokin, D.; Wulff, L., String instanton in ads_{4} × CP \^{}{3}, JHEP, 05, 009, (2010) · Zbl 1288.81097 · doi:10.1007/JHEP05(2010)009 |
| [30] | Sorokin, D.; Tseytlin, A.; Wulff, L.; Zarembo, K., Superstrings in ads_{2} × S\^{}{2} × T\^{}{6}, J. Phys., A 44, 275401, (2011) · Zbl 1220.81166 |
| [31] | Sorokin, D.; Wulff, L., Evidence for the classical integrability of the complete ads_{4} × CP\^{}{3} superstring, JHEP, 11, 143, (2010) · Zbl 1294.81235 · doi:10.1007/JHEP11(2010)143 |
| [32] | Cagnazzo, A.; Sorokin, D.; Wulff, L., More on integrable structures of superstrings in ads_{4} × CP \^{}{3} and ads_{2} × S\^{}{2} × T \^{}{6} superbackgrounds, JHEP, 01, 004, (2012) · Zbl 1306.81202 · doi:10.1007/JHEP01(2012)004 |
| [33] | Uvarov, DV, Kaluza-Klein gauge and minimal integrable extension of \( \text{OSp}\left( {4|6} \right)/\left( {\text{SO}\left( {1,\;3} \right) × \text{U}(3)} \right) \) σ-model, Int. J. Mod. Phys., A 27, 1250118, (2012) · Zbl 1260.81211 |
| [34] | Ohlsson Sax, O.; Stefanski, B., Integrability, spin-chains and the ads_{3}/CF T_{2} correspondence, JHEP, 08, 029, (2011) · Zbl 1298.81328 |
| [35] | Zarembo, K., Worldsheet spectrum in ads_{4}/CF T_{3} correspondence, JHEP, 04, 135, (2009) · doi:10.1088/1126-6708/2009/04/135 |
| [36] | Sundin, P., On the worldsheet theory of the type IIA ads_{4} × CP \^{}{3} superstring, JHEP, 04, 014, (2010) · Zbl 1272.81173 · doi:10.1007/JHEP04(2010)014 |
| [37] | Zarembo, K.; Zieme, S., Fine structure of string spectrum in ads_{5} × S\^{}{5}, JETP Lett., 95, 219, (2012) · doi:10.1134/S0021364012050116 |
| [38] | Tseytlin, AA, On Dilaton dependence of type-II superstring action, Class. Quant. Grav., 13, l81, (1996) · Zbl 0856.53081 · doi:10.1088/0264-9381/13/6/003 |
| [39] | Cvetič, M.; Lü, H.; Pope, C.; Stelle, K., T duality in the Green-Schwarz formalism and the massless/massive IIA duality map, Nucl. Phys., B 573, 149, (2000) · Zbl 0947.81095 |
| [40] | Berenstein, DE; Maldacena, JM; Nastase, HS, Strings in flat space and pp waves from N =4 super Yang-Mills, JHEP, 04, 013, (2002) · doi:10.1088/1126-6708/2002/04/013 |
| [41] | Frolov, S.; Plefka, J.; Zamaklar, M., The ads_{5} × S\^{}{5} superstring in light-cone gauge and its Bethe equations, J. Phys., A 39, 13037, (2006) · Zbl 1112.83055 |
| [42] | Hentschel, A.; Plefka, J.; Sundin, P., Testing the nested light-cone Bethe equations of the ads_{5} × S\^{}{5} superstring, JHEP, 05, 021, (2007) · doi:10.1088/1126-6708/2007/05/021 |
| [43] | Astolfi, D.; Puletti, VGM; Grignani, G.; Harmark, T.; Orselli, M., Finite-size corrections in the SU(2) × SU(2) sector of type IIA string theory on ads_{4} × CP \^{}{3}, Nucl. Phys., B 810, 150, (2009) · Zbl 1323.81073 · doi:10.1016/j.nuclphysb.2008.10.020 |
| [44] | Sundin, P., The ads_{4} × CP \^{}{3} string and its Bethe equations in the near plane wave limit, JHEP, 02, 046, (2009) · Zbl 1245.81226 · doi:10.1088/1126-6708/2009/02/046 |
| [45] | Abbott, MC; Sundin, P.; Sundin, P., The near-flat-space and BMN limits for strings in ads_{4} × CP \^{}{3} at one loop, J. Phys., A 45, 025401, (2012) · Zbl 1267.81262 |
| [46] | Giombi, S.; Ricci, R.; Roiban, R.; Tseytlin, A., Quantum dispersion relations for excitations of long folded spinning superstring in ads_{5} × S\^{}{5}, JHEP, 01, 128, (2011) · Zbl 1214.81212 · doi:10.1007/JHEP01(2011)128 |
| [47] | Beisert, N.; etal., Review of AdS/CFT integrability: an overview, Lett. Math. Phys., 99, 3, (2012) · Zbl 1268.81126 · doi:10.1007/s11005-011-0529-2 |
| [48] | Nishioka, T.; Takayanagi, T., On type IIA Penrose limit and N = 6 Chern-Simons theories, JHEP, 08, 001, (2008) · doi:10.1088/1126-6708/2008/08/001 |
| [49] | Gaiotto, D.; Giombi, S.; Yin, X., Spin chains in N = 6 superconformal Chern-Simons-matter theory, JHEP, 04, 066, (2009) · doi:10.1088/1126-6708/2009/04/066 |
| [50] | Grignani, G.; Harmark, T.; Orselli, M., The SU(2) × SU(2) sector in the string dual of N =6 superconformal Chern-Simons theory, Nucl. Phys., B 810, 115, (2009) · Zbl 1192.81269 · doi:10.1016/j.nuclphysb.2008.10.019 |
| [51] | Gromov, N.; Mikhaylov, V., Comment on the scaling function in ads_{4} × CP \^{}{3}, JHEP, 04, 083, (2009) · doi:10.1088/1126-6708/2009/04/083 |
| [52] | Astolfi, D.; Puletti, VGM; Grignani, G.; Harmark, T.; Orselli, M., Finite-size corrections for quantum strings on ads_{4} × CP \^{}{3}, JHEP, 05, 128, (2011) · Zbl 1296.81077 · doi:10.1007/JHEP05(2011)128 |
| [53] | Astolfi, D.; Grignani, G.; Ser-Giacomi, E.; Zayakin, A., Strings in ads_{4} × CP\^{}{3}: finite size spectrum vs. Bethe ansatz, JHEP, 04, 005, (2012) · Zbl 1348.81349 · doi:10.1007/JHEP04(2012)005 |
| [54] | McLoughlin, T.; Roiban, R., Spinning strings at one-loop in ads_{4} × p\^{}{3}, JHEP, 12, 101, (2008) · Zbl 1329.81319 · doi:10.1088/1126-6708/2008/12/101 |
| [55] | Alday, LF; Arutyunov, G.; Bykov, D., Semiclassical quantization of spinning strings in ads_{4} × CP \^{}{3}, JHEP, 11, 089, (2008) · doi:10.1088/1126-6708/2008/11/089 |
| [56] | Krishnan, C., Ads_{4}/CF T_{3} at one loop, JHEP, 09, 092, (2008) · Zbl 1245.81197 · doi:10.1088/1126-6708/2008/09/092 |
| [57] | McLoughlin, T.; Roiban, R.; Tseytlin, AA, Quantum spinning strings in ads_{4} × CP \^{}{3}: testing the Bethe ansatz proposal, JHEP, 11, 069, (2008) · doi:10.1088/1126-6708/2008/11/069 |
| [58] | Bandres, MA; Lipstein, AE, One-loop corrections to type IIA string theory in ads_{4} × CP \^{}{3}, JHEP, 04, 059, (2010) · Zbl 1272.81136 · doi:10.1007/JHEP04(2010)059 |
| [59] | I. Shenderovich, Giant magnons in AdS_{4}/CF T_{3}: dispersion, quantization and finite-size corrections, arXiv:0807.2861 [INSPIRE]. |
| [60] | Abbott, MC; Aniceto, I.; Bombardelli, D., Quantum strings and the ads_{4}/CF T_{3} interpolating function, JHEP, 12, 040, (2010) · Zbl 1294.81129 · doi:10.1007/JHEP12(2010)040 |
| [61] | Beccaria, M.; Macorini, G.; Ratti, C.; Valatka, S., Semiclassical folded string in ads_{5} × S\^{}{5}, JHEP, 05, 030, (2012) · Zbl 1348.81309 · doi:10.1007/JHEP05(2012)030 |
| [62] | C. Lopez-Arcos and H. Nastase, Eliminating ambiguities for quantum corrections to strings moving in AdS_{4} × CP\^{}{3}, arXiv:1203.4777 [INSPIRE]. · Zbl 1272.81160 |
| [63] | V.A. Smirnov, Feynman integral calculus, Springer, U.S.A. (2006). · Zbl 1111.81003 |
| [64] | Callan, CG; McLoughlin, T.; Swanson, I., Higher impurity AdS/CFT correspondence in the near-BMN limit, Nucl. Phys., B 700, 271, (2004) · Zbl 1123.81391 · doi:10.1016/j.nuclphysb.2004.08.025 |
| [65] | J. Murugan, P. Sundin and L. Wulff, Classical and quantum aspects of the AdS_{2} × \(S\)\^{}{2} × \(T\)\^{}{6}string, in preparation. · Zbl 1342.81461 |
| [66] | P. Sundin, Perturbative quantization of superstring theory in Anti de-Sitter spaces, Ph.D. thesis, Humboldt University, Berlin, Germany (2010). |
| [67] | V. Forini, V.G.M. Puletti and O. Ohlsson Sax, Generalized cusp in AdS_{4} × CP\^{}{3}and more one-loop results from semiclassical strings, arXiv:1204.3302 [INSPIRE]. · Zbl 1276.81105 |
| [68] | Ferreira, LC; Cherchiglia, A.; Hiller, B.; Sampaio, M.; Nemes, M., Momentum routing invariance in Feynman diagrams and quantum symmetry breakings, Phys. Rev., D 86, 025016, (2012) |
| [69] | Ahn, C.; Nepomechie, RI, N = 6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations, JHEP, 09, 010, (2008) · Zbl 1245.81255 · doi:10.1088/1126-6708/2008/09/010 |
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