Bianchi, Lorenzo; Forini, Valentina; Hoare, Ben Two-dimensional S-matrices from unitarity cuts. (English) Zbl 1342.81647 J. High Energy Phys. 2013, No. 7, Paper No. 088, 23 p. (2013). Summary: Using unitarity methods, we compute, for several massive two-dimensional models, the cut-constructible part of the one-loop \(2 \to 2\) scattering S-matrices from the tree-level amplitudes. We apply our method to various integrable theories, finding evidence that for supersymmetric models the one-loop S-matrix is cut-constructible, while for models without supersymmetry (but with integrability) the missing rational terms are proportional to the tree-level S-matrix and therefore can be interpreted as a shift in the coupling. Finally, applying our procedure to the world-sheet theory for the light-cone gauge-fixed \(\mathrm{AdS}_5\times S^5\) superstring we reproduce, at one-loop in the near-BMN expansion, the S-matrix known from integrability techniques. Cited in 24 Documents MSC: 81U20 \(S\)-matrix theory, etc. in quantum theory 81R12 Groups and algebras in quantum theory and relations with integrable systems 81T99 Quantum field theory; related classical field theories 81V99 Applications of quantum theory to specific physical systems Keywords:field theories in lower dimensions; AdS-CFT correspondence; integrable field theories PDFBibTeX XMLCite \textit{L. Bianchi} et al., J. High Energy Phys. 2013, No. 7, Paper No. 088, 23 p. (2013; Zbl 1342.81647) Full Text: DOI arXiv References: [1] R. Roiban, M. Spradlin and A. Volovich, Scattering amplitudes in gauge theories: progress and outlook, J. Phys.A 44 (2011) 450301. [2] N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys.12 (2008) 945 [hep-th/0511082] [INSPIRE]. [3] G. Arutyunov and S. Frolov, Foundations of the AdS5 × S5superstring. Part I, J. Phys.A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE]. · Zbl 1167.81028 [4] N. Beisert et al., Review of AdS/CFT integrability: an overview, Lett. Math. Phys.99 (2012) 3 [arXiv:1012.3982] [INSPIRE]. [5] T. Klose and K. Zarembo, Bethe ansatz in stringy σ-models, J. Stat. Mech.0605 (2006) P05006 [hep-th/0603039] [INSPIRE]. · Zbl 1456.81337 [6] R. Roiban, A. Tirziu and A.A. Tseytlin, Asymptotic Bethe ansatz S-matrix and Landau-Lifshitz type effective 2D actions, J. Phys.A 39 (2006) 13129 [hep-th/0604199] [INSPIRE]. · Zbl 1109.81071 [7] T. Klose, T. McLoughlin, R. Roiban and K. Zarembo, Worldsheet scattering in AdS5 × S5, JHEP03 (2007) 094 [hep-th/0611169] [INSPIRE]. [8] T. Klose and K. Zarembo, Reduced σ-model on AdS5 × S5: one-loop scattering amplitudes, JHEP02 (2007) 071 [hep-th/0701240] [INSPIRE]. [9] T. Klose, T. McLoughlin, J. Minahan and K. Zarembo, World-sheet scattering in AdS5 × S5at two loops, JHEP08 (2007) 051 [arXiv:0704.3891] [INSPIRE]. · Zbl 1326.81161 [10] A.B. Zamolodchikov and A.B. Zamolodchikov, Factorized s matrices in two-dimensions as the exact solutions of certain relativistic quantum field models, Annals Phys.120 (1979) 253 [INSPIRE]. [11] E. Ogievetsky, P. Wiegmann and N. Reshetikhin, The principal chiral field in two-dimensions on classical Lie algebras: the Bethe ansatz solution and factorized theory of scattering, Nucl. Phys.B 280 (1987) 45 [INSPIRE]. [12] P. Dorey, Exact S matrices, hep-th/9810026 [INSPIRE]. · Zbl 0917.35133 [13] I. Arefeva and V. Korepin, Scattering in two-dimensional model with lagrangian (1/γ)((∂μu)2/2 + m2 cos(u − 1)), Pisma Zh. Eksp. Teor. Fiz.20 (1974) 680 [INSPIRE]. [14] R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys.B 725 (2005) 275 [hep-th/0412103] [INSPIRE]. · Zbl 1178.81202 [15] Z. Bern and Y.-t. Huang, Basics of generalized unitarity, J. Phys.A 44 (2011) 454003 [arXiv:1103.1869] [INSPIRE]. · Zbl 1270.81209 [16] W. van Neerven, Dimensional regularization of mass and infrared singularities in two loop on-shell vertex functions, Nucl. Phys.B 268 (1986) 453 [INSPIRE]. [17] Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys.B 425 (1994) 217 [hep-ph/9403226] [INSPIRE]. · Zbl 1049.81644 [18] Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys.B 435 (1995) 59 [hep-ph/9409265] [INSPIRE]. [19] L.J. Dixon, Calculating scattering amplitudes efficiently, hep-ph/9601359 [INSPIRE]. [20] R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The analytic S-matrix, Cambridge Univeristy Press, Cambridge U.K. (2002). · Zbl 0139.46204 [21] Z. Bern, J. Rozowsky and B. Yan, Two loop four gluon amplitudes in N = 4 super Yang-Mills, Phys. Lett.B 401 (1997) 273 [hep-ph/9702424] [INSPIRE]. [22] Z. Bern and A. Morgan, Massive loop amplitudes from unitarity, Nucl. Phys.B 467 (1996) 479 [hep-ph/9511336] [INSPIRE]. [23] T.J. Hollowood, J.L. Miramontes and Q.-H. Park, Massive integrable soliton theories, Nucl. Phys.B 445 (1995) 451 [hep-th/9412062] [INSPIRE]. · Zbl 1009.81565 [24] I. Bakas, Q.-H. Park and H.-J. Shin, Lagrangian formulation of symmetric space sine-Gordon models, Phys. Lett.B 372 (1996) 45 [hep-th/9512030] [INSPIRE]. · Zbl 1036.81513 [25] N. Dorey and T.J. Hollowood, Quantum scattering of charged solitons in the complex sine-Gordon model, Nucl. Phys.B 440 (1995) 215 [hep-th/9410140] [INSPIRE]. · Zbl 0990.81704 [26] B. Hoare and A. Tseytlin, On the perturbative S-matrix of generalized sine-Gordon models, JHEP11 (2010) 111 [arXiv:1008.4914] [INSPIRE]. · Zbl 1294.81262 [27] H. de Vega and J. Maillet, Renormalization character and quantum S matrix for a classically integrable theory, Phys. Lett.B 101 (1981) 302 [INSPIRE]. [28] T.J. Hollowood and J.L. Miramontes, Classical and quantum solitons in the symmetric space sine-Gordon theories, JHEP04 (2011) 119 [arXiv:1012.0716] [INSPIRE]. · Zbl 1250.81047 [29] G. Felder, Elliptic quantum groups, hep-th/9412207 [INSPIRE]. · Zbl 0998.17015 [30] B. Hoare, T.J. Hollowood and J.L. Miramontes, Restoring unitarity in the q-deformed world-sheet S-matrix, arXiv:1303.1447 [INSPIRE]. [31] E. Witten, Nonabelian bosonization in two-dimensions, Commun. Math. Phys.92 (1984) 455. · Zbl 0536.58012 [32] V. Knizhnik and A. Zamolodchikov, Current algebra and Wess-Zumino model in two-dimensions, Nucl. Phys.B 247 (1984) 83 [INSPIRE]. · Zbl 0661.17020 [33] H. Leutwyler and M.A. Shifman, Perturbation theory in the Wess-Zumino-Novikov-Witten model, Int. J. Mod. Phys.A 7 (1992) 795 [INSPIRE]. [34] A.A. Tseytlin, Effective action of gauged WZW model and exact string solutions, Nucl. Phys.B 399 (1993) 601 [hep-th/9301015] [INSPIRE]. [35] A.A. Tseytlin, Conformal σ-models corresponding to gauged Wess-Zumino-Witten theories, Nucl. Phys.B 411 (1994) 509 [hep-th/9302083] [INSPIRE]. · Zbl 1049.81560 [36] B. de Wit, M.T. Grisaru and P. van Nieuwenhuizen, The WZNW model at two loops, Nucl. Phys.B 408 (1993) 299 [hep-th/9307027] [INSPIRE]. · Zbl 1043.81704 [37] K. Pohlmeyer, Integrable hamiltonian systems and interactions through quadratic constraints, Commun. Math. Phys.46 (1976) 207. · Zbl 0996.37504 [38] H. Eichenherr and K. Pohlmeyer, Lax pairs for certain generalizations of the sine-Gordon equation, Phys. Lett.B 89 (1979) 76 [INSPIRE]. [39] A.A. Tseytlin, Spinning strings and AdS/CFT duality, hep-th/0311139 [INSPIRE]. · Zbl 1080.81055 [40] B. Barbashov and V. Nesterenko, Relativistic string model in a space-time of a constant curvature, Commun. Math. Phys.78 (1981) 499. · Zbl 0465.53019 [41] H. De Vega and N.G. Sanchez, Exact integrability of strings in D-Dimensional de Sitter space-time, Phys. Rev.D 47 (1993) 3394 [INSPIRE]. [42] R. Metsaev and A.A. Tseytlin, Type IIB superstring action in AdS5 × S5background, Nucl. Phys.B 533 (1998) 109 [hep-th/9805028] [INSPIRE]. · Zbl 0956.81063 [43] M. Grigoriev and A.A. Tseytlin, Pohlmeyer reduction of AdS5 × S5superstring σ-model, Nucl. Phys.B 800 (2008) 450 [arXiv:0711.0155] [INSPIRE]. · Zbl 1292.81114 [44] A. Mikhailov and S. Schäfer-Nameki, Sine-Gordon-like action for the Superstring in AdS5 × S5, JHEP05 (2008) 075 [arXiv:0711.0195] [INSPIRE]. [45] M. Grigoriev and A.A. Tseytlin, On reduced models for superstrings on AdSn × Sn, Int. J. Mod. Phys.A 23 (2008) 2107 [arXiv:0806.2623] [INSPIRE]. [46] A. Babichenko, B. Stefanski Jr. and K. Zarembo, Integrability and the AdS3/CFT2correspondence, JHEP03 (2010) 058 [arXiv:0912.1723] [INSPIRE]. · Zbl 1271.81118 [47] D. Sorokin, A. Tseytlin, L. Wulff and K. Zarembo, Superstrings in AdS2 × S2 × T6, J. Phys.A 44 (2011) 275401 [arXiv:1104.1793] [INSPIRE]. [48] R. Roiban and A.A. Tseytlin, UV finiteness of Pohlmeyer-reduced form of the AdS5 × S5superstring theory, JHEP04 (2009) 078 [arXiv:0902.2489] [INSPIRE]. [49] D.M. Schmidtt, Supersymmetry flows, semi-symmetric space sine-Gordon models and the Pohlmeyer reduction, JHEP03 (2011) 021 [arXiv:1012.4713] [INSPIRE]. · Zbl 1301.81265 [50] T.J. Hollowood and J.L. Miramontes, The AdS5 × S5semi-symmetric space sine-Gordon theory, JHEP05 (2011) 136 [arXiv:1104.2429] [INSPIRE]. · Zbl 1296.81102 [51] M. Goykhman and E. Ivanov, Worldsheet Supersymmetry of Pohlmeyer-reduced AdSn × Snsuperstrings, JHEP09 (2011) 078 [arXiv:1104.0706] [INSPIRE]. · Zbl 1301.81215 [52] D.M. Schmidtt, Integrability vs. supersymmetry: Poisson structures of the Pohlmeyer reduction, JHEP11 (2011) 067 [arXiv:1106.4796] [INSPIRE]. · Zbl 1306.81276 [53] B. Hoare and A. Tseytlin, Tree-level S-matrix of Pohlmeyer reduced form of AdS5 × S5superstring theory, JHEP02 (2010) 094 [arXiv:0912.2958] [INSPIRE]. · Zbl 1270.81175 [54] B. Hoare and A. Tseytlin, Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS5 × S5superstring theory, Nucl. Phys.B 851 (2011) 161 [arXiv:1104.2423] [INSPIRE]. · Zbl 1229.81237 [55] K.-i. Kobayashi and T. Uematsu, S matrix of N = 2 supersymmetric sine-Gordon theory, Phys. Lett.B 275 (1992) 361 [hep-th/9110040] [INSPIRE]. [56] R. Shankar and E. Witten, The S matrix of the supersymmetric nonlinear σ-model, Phys. Rev.D 17 (1978) 2134 [INSPIRE]. [57] I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS5 × S5superstring, Phys. Rev.D 69 (2004) 046002 [hep-th/0305116] [INSPIRE]. [58] V. Kazakov, A. Marshakov, J. Minahan and K. Zarembo, Classical/quantum integrability in AdS/CFT, JHEP05 (2004) 024 [hep-th/0402207] [INSPIRE]. [59] N. Berkovits, Quantum consistency of the superstring in AdS5 × S5background, JHEP03 (2005) 041 [hep-th/0411170] [INSPIRE]. [60] G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP10 (2004) 016 [hep-th/0406256] [INSPIRE]. [61] R.A. Janik, The AdS5 × S5superstring worldsheet S-matrix and crossing symmetry, Phys. Rev.D 73 (2006) 086006 [hep-th/0603038] [INSPIRE]. [62] D. Volin, Minimal solution of the AdS/CFT crossing equation, J. Phys.A 42 (2009) 372001 [arXiv:0904.4929] [INSPIRE]. · Zbl 1176.81106 [63] N. Beisert, R. Hernandez and E. Lopez, A crossing-symmetric phase for AdS5 × S5strings, JHEP11 (2006) 070 [hep-th/0609044] [INSPIRE]. [64] N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech.0701 (2007) P01021 [hep-th/0610251] [INSPIRE]. [65] T. McLoughlin, Review of AdS/CFT Integrability, Chapter II.2: quantum strings in AdS5 × S5, Lett. Math. Phys.99 (2012) 127 [arXiv:1012.3987] [INSPIRE]. · Zbl 1244.81055 [66] G. Arutyunov, S. Frolov, J. Plefka and M. Zamaklar, The off-shell symmetry algebra of the light-cone AdS5 × S5superstring, J. Phys.A 40 (2007) 3583 [hep-th/0609157] [INSPIRE]. · Zbl 1113.81106 [67] G. Arutyunov, S. Frolov and M. Zamaklar, Finite-size effects from giant magnons, Nucl. Phys.B 778 (2007) 1 [hep-th/0606126] [INSPIRE]. · Zbl 1200.83114 [68] S. Frolov, J. Plefka and M. Zamaklar, The AdS5 × S5superstring in light-cone gauge and its Bethe equations, J. Phys.A 39 (2006) 13037 [hep-th/0603008] [INSPIRE]. · Zbl 1112.83055 [69] R. Roiban, A. Tirziu and A.A. Tseytlin, Two-loop world-sheet corrections in AdS5 × S5superstring, JHEP07 (2007) 056 [arXiv:0704.3638] [INSPIRE]. [70] J.M. Maldacena and I. Swanson, Connecting giant magnons to the pp-wave: an interpolating limit of AdS5 × S5, Phys. Rev.D 76 (2007) 026002 [hep-th/0612079] [INSPIRE]. [71] V. Giangreco Marotta Puletti, T. Klose and O. Ohlsson Sax, Factorized world-sheet scattering in near-flat AdS5 × S5, Nucl. Phys.B 792 (2008) 228 [arXiv:0707.2082] [INSPIRE]. · Zbl 1225.81105 [72] G. Arutyunov, S. Frolov and M. Zamaklar, The Zamolodchikov-Faddeev algebra for AdS5 × S5superstring, JHEP04 (2007) 002 [hep-th/0612229] [INSPIRE]. [73] N. Beisert, V. Dippel and M. Staudacher, A novel long range spin chain and planar N = 4 super Yang-Mills, JHEP07 (2004) 075 [hep-th/0405001] [INSPIRE]. [74] G. Arutyunov and S. Frolov, On AdS5 × S5string S-matrix, Phys. Lett.B 639 (2006) 378 [hep-th/0604043] [INSPIRE]. [75] C. Ahn and R.I. Nepomechie, Review of AdS/CFT integrability, chapter III.2: exact world-sheet S-matrix, Lett. Math. Phys.99 (2012) 209 [arXiv:1012.3991] [INSPIRE]. · Zbl 1244.81048 [76] K. Zarembo, Strings on semisymmetric superspaces, JHEP05 (2010) 002 [arXiv:1003.0465] [INSPIRE]. · Zbl 1288.81127 [77] A. Cagnazzo and K. Zarembo, B-field in AdS3/CFT2correspondence and integrability, JHEP11 (2012)133 [Erratum ibid.1304 (2013) 003] [arXiv:1209.4049] [INSPIRE]. · Zbl 1342.81482 [78] K. Zarembo, Worldsheet spectrum in AdS4/CFT3correspondence, JHEP04 (2009) 135 [arXiv:0903.1747] [INSPIRE]. [79] C. Kalousios, C. Vergu and A. Volovich, Factorized tree-level scattering in AdS4 × CP3, JHEP09 (2009) 049 [arXiv:0905.4702] [INSPIRE]. [80] N. Rughoonauth, P. Sundin and L. Wulff, Near BMN dynamics of the AdS3 × S3 × S3 × S1superstring, JHEP07 (2012) 159 [arXiv:1204.4742] [INSPIRE]. [81] P. Sundin and L. Wulff, Worldsheet scattering in AdS3/CFT2, JHEP07 (2013) 007 [arXiv:1302.5349] [INSPIRE]. · Zbl 1342.83428 [82] B. Hoare and A. Tseytlin, On string theory on AdS3 × S3 × T4with mixed 3-form flux: tree-level S-matrix, Nucl. Phys.B 873 (2013) 682 [arXiv:1303.1037] [INSPIRE]. · Zbl 1282.81146 [83] T. Klose and T. McLoughlin, Worldsheet form factors in AdS/CFT, Phys. Rev.D 87 (2013) 026004 [arXiv:1208.2020] [INSPIRE]. [84] O.T. Engelund, R.W. McKeown and R. Roiban, Generalized unitarity and the worldsheet S matrix in AdSn × Sn × M10−2n, arXiv:1304.4281 [INSPIRE]. · Zbl 1342.83363 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.