Abstract
We compute the full one-loop 2-particle S-matrix for excitations of the type IIB AdS 3 × S 3 × T 4 BMN string. The S-matrix is found to respect the expected symmetries and the phases are consistent with the crossing equations. By analyzing how the relevant integrals scale with the IR regulator we show that scattering of massless bosons is trivial at two loops. Based on our results we argue that the additional su(2) S-matrix appearing in the massless sector in the exact solution should trivialize.
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References
L. Wulff, On integrability of strings on symmetric spaces, JHEP 09 (2015) 115 [arXiv:1505.03525] [INSPIRE].
A. Babichenko, B. Stefanski Jr. and K. Zarembo, Integrability and the AdS 3 /CF T 2 correspondence, JHEP 03 (2010) 058 [arXiv:0912.1723] [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].
A. Cagnazzo and K. Zarembo, B-field in AdS 3 /CF T 2 correspondence and integrability, JHEP 11 (2012) 133 [Erratum ibid. 1304 (2013) 003] [arXiv:1209.4049] [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].
L. Wulff, Superisometries and integrability of superstrings, JHEP 05 (2014) 115 [arXiv:1402.3122] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefanski, The complete AdS 3 × S 3 × T 4 worldsheet S matrix, JHEP 10 (2014) 66 [arXiv:1406.0453] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefanski Jr. and A. Torrielli, Dressing phases of AdS3/CFT2, Phys. Rev. D 88 (2013) 066004 [arXiv:1306.2512] [INSPIRE].
P. Sundin and L. Wulff, Worldsheet scattering in AdS 3 /CF T 2, JHEP 07 (2013) 007 [arXiv:1302.5349] [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].
M.C. Abbott, The AdS 3 × S 3 × S 3 × S 1 Hernández-López phases: a semiclassical derivation, J. Phys. A 46 (2013) 445401 [arXiv:1306.5106] [INSPIRE].
L. Bianchi and B. Hoare, AdS 3 × S 3 × M 4 string S-matrices from unitarity cuts, JHEP 08 (2014) 097 [arXiv:1405.7947] [INSPIRE].
R. Roiban, P. Sundin, A. Tseytlin and L. Wulff, The one-loop worldsheet S-matrix for the AdS n × S n × T 10−2n superstring, JHEP 08 (2014) 160 [arXiv:1407.7883] [INSPIRE].
P. Sundin and L. Wulff, The AdS n × S n × T 10−2n BMN string at two loops, JHEP 11 (2015) 154 [arXiv:1508.04313] [INSPIRE].
R. Borsato, O.O. Sax, A. Sfondrini and B. Stefanski, On the spectrum of AdS 3 × S 3 × T 4 strings with Ramond-Ramond flux, arXiv:1605.00518 [INSPIRE].
M. C. Abbott and I. Aniceto, Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz, arXiv:1512.08761 [INSPIRE].
P. Sundin and L. Wulff, One- and two-loop checks for the AdS 3 × S 3 × T 4 superstring with mixed flux, J. Phys. A 48 (2015) 105402 [arXiv:1411.4662] [INSPIRE].
L. Wulff, The type-II superstring to order θ 4, JHEP 07 (2013) 123 [arXiv:1304.6422] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N =4 super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
L. Bianchi and M.S. Bianchi, On the scattering of gluons in the GKP string, JHEP 02 (2016) 146 [arXiv:1511.01091] [INSPIRE].
K. Zarembo, Worldsheet spectrum in AdS 4 /CF T 3 correspondence, JHEP 04 (2009) 135 [arXiv:0903.1747] [INSPIRE].
O. Ohlsson Sax and B. Stefanski Jr., Integrability, spin-chains and the AdS3/CFT2 correspondence, JHEP 08 (2011) 029 [arXiv:1106.2558] [INSPIRE].
O. Ohlsson Sax, B. Stefanski Jr. and A. Torrielli, On the massless modes of the AdS3/CFT2 integrable systems, JHEP 03 (2013) 109 [arXiv:1211.1952] [INSPIRE].
B. Hoare, A. Stepanchuk and A.A. Tseytlin, Giant magnon solution and dispersion relation in string theory in AdS 3 × S 3 × T 4 with mixed flux, Nucl. Phys. B 879 (2014) 318 [arXiv:1311.1794] [INSPIRE].
T. Lloyd, O. Ohlsson Sax, A. Sfondrini and B. Stefanski Jr., The complete worldsheet S matrix of superstrings on AdS 3 × S 3 × T 4 with mixed three-form flux, Nucl. Phys. B 891 (2015) 570 [arXiv:1410.0866] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefanski and A. Torrielli, The all-loop integrable spin-chain for strings on AdS 3 × S 3 × T 4 : the massive sector, JHEP 08 (2013) 043 [arXiv:1303.5995] [INSPIRE].
T. Klose, T. McLoughlin, J.A. Minahan and K. Zarembo, World-sheet scattering in AdS 5 × S 5 at two loops, JHEP 08 (2007) 051 [arXiv:0704.3891] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefanski, Towards the All-Loop Worldsheet S Matrix for AdS 3 × S 3 × T 4, Phys. Rev. Lett. 113 (2014) 131601 [arXiv:1403.4543] [INSPIRE].
M.C. Abbott, Comment on Strings in AdS 3 × S 3 × S 3 × S 1 at One Loop, JHEP 02 (2013) 102 [arXiv:1211.5587] [INSPIRE].
M. Beccaria, F. Levkovich-Maslyuk, G. Macorini and A.A. Tseytlin, Quantum corrections to spinning superstrings in AdS 3 × S 3 × M 4 : determining the dressing phase, JHEP 04 (2013) 006 [arXiv:1211.6090] [INSPIRE].
R. Borsato, O. Ohlsson Sax and A. Sfondrini, All-loop Bethe ansatz equations for AdS3/CFT2, JHEP 04 (2013) 116 [arXiv:1212.0505] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefanski, The AdS3 × S3 × S3 × S1 worldsheet S matrix, J. Phys. A 48 (2015) 415401 [arXiv:1506.00218] [INSPIRE].
N. Rughoonauth, P. Sundin and L. Wulff, Near BMN dynamics of the AdS 3 × S 3 × S 3 × S 1 superstring, JHEP 07 (2012) 159 [arXiv:1204.4742] [INSPIRE].
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ArXiv ePrint: 1605.01632
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Sundin, P., Wulff, L. The complete one-loop BMN S-matrix in AdS 3 × S 3 × T 4 . J. High Energ. Phys. 2016, 62 (2016). https://doi.org/10.1007/JHEP06(2016)062
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DOI: https://doi.org/10.1007/JHEP06(2016)062