Abstract
We compute the massive-sector worldsheet S-matrix for superstring theories in AdS n × S n × T 10−2n (with n = 2, 3, 5) in the near BMN expansion up to one-loop order in inverse string tension. We show that, after taking into account the wave function renormalization, the one-loop S-matrix is UV finite. In an appropriate regularization scheme the S-matrix is consistent with the underlying symmetries of the superstring theory, i.e. for the n=3,5casesitcoincideswiththeoneimpliedbythelight-conegaugesymmetrieswiththe dressing phases determined from the crossing equations. For the n = 2, 3 cases we observe that the massless modes decouple from the one-loop calculation of massive mode scattering, i.e. the 2n-dimensional supercoset sigma model and the full 10-dimensional superstring happen to have the same massive one-loop S-matrix.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
A. Babichenko, B. Stefanski Jr. and K. Zarembo, Integrability and the AdS 3 /CFT 2 correspondence, JHEP 03 (2010) 058 [arXiv:0912.1723] [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].
V.N. Velizhanin, Vanishing of the four-loop charge renormalization function in N = 4 SYM theory, Phys. Lett. B 696 (2011) 560 [arXiv:1008.2198] [INSPIRE].
J.M. Maldacena and I. Swanson, Connecting giant magnons to the pp-wave: an interpolating limit of AdS 5 × S 5, Phys. Rev. D 76 (2007) 026002 [hep-th/0612079] [INSPIRE].
T. Klose and K. Zarembo, Reduced σ-model on AdS 5 × S 5 : one-loop scattering amplitudes, JHEP 02 (2007) 071 [hep-th/0701240] [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].
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].
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].
P. Sundin and L. Wulff, Worldsheet scattering in AdS 3 /CFT 2, JHEP 07 (2013) 007 [arXiv:1302.5349] [INSPIRE].
J. Murugan, P. Sundin and L. Wulff, Classical and quantum integrability in AdS 2 /CFT 1, JHEP 01 (2013) 047 [arXiv:1209.6062] [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].
L. Bianchi, V. Forini and B. Hoare, Two-dimensional S-matrices from unitarity cuts, JHEP 07 (2013) 088 [arXiv:1304.1798] [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].
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].
P. Sundin, Worldsheet two- and four-point functions at one loop in AdS 3 /CFT 2, Phys. Lett. B 733 (2014) 134 [arXiv:1403.1449] [INSPIRE].
B. Hoare, A. Pittelli and A. Torrielli, S-matrix for the massive and massless modes of the AdS 2 × S 2 superstring, arXiv:1407.0303 [INSPIRE].
G. Arutyunov, S. Frolov and M. Zamaklar, Finite-size effects from giant magnons, Nucl. Phys. B 778 (2007) 1 [hep-th/0606126] [INSPIRE].
J. Zinn-Justin, Quantum field theory and critical phenomena, Int. Ser. Monogr. Phys. 113 (2002)1 [INSPIRE].
H.J. de Vega and J.M. Maillet, Renormalization character and quantum S matrix for a classically integrable theory, Phys. Lett. B 101 (1981) 302 [INSPIRE].
H.J. de Vega and J.M. Maillet, Semiclassical quantization of the complex sine-Gordon field theory, Phys. Rev. D 28 (1983) 1441 [INSPIRE].
B. Hoare and A.A. Tseytlin, On the perturbative S-matrix of generalized sine-Gordon models, JHEP 11 (2010) 111 [arXiv:1008.4914] [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. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefanski, The complete AdS 3 × S 3 × T 4 worldsheet S-matrix, arXiv:1406.0453 [INSPIRE].
R.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].
L. Wulff, The type-II superstring to order θ 4, JHEP 07 (2013) 123 [arXiv:1304.6422] [INSPIRE].
L. Wulff, Superisometries and integrability of superstrings, arXiv:1402.3122 [INSPIRE].
R. Kallosh, J. Rahmfeld and A. Rajaraman, Near horizon superspace, JHEP 09 (1998) 002 [hep-th/9805217] [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].
R. Hernandez and E. Lopez, Quantum corrections to the string Bethe ansatz, JHEP 07 (2006) 004 [hep-th/0603204] [INSPIRE].
N. Beisert, R. Hernandez and E. Lopez, A crossing-symmetric phase for AdS 5 × S 5 strings, JHEP 11 (2006) 070 [hep-th/0609044] [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 AdS 3 /CFT 2, JHEP 04 (2013) 116 [arXiv:1212.0505] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefanski Jr. and A. Torrielli, Dressing phases of AdS 3 /CFT 2, Phys. Rev. D 88 (2013) 066004 [arXiv:1306.2512] [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].
A.A. Belavin, A direct calculation of the spectrum of masses in an integrable model from the Hopf algebra symmetry, Phys. Lett. B 283 (1992) 67 [INSPIRE].
T. Curtright and C.K. Zachos, Supersymmetry and the nonlocal Yangian deformation symmetry, Nucl. Phys. B 402 (1993) 604 [hep-th/9210060] [INSPIRE].
A. Cagnazzo and K. Zarembo, B-field in AdS 3 /CFT 2 correspondence and integrability, JHEP 11 (2012) 133 [Erratum ibid. 04 (2013) 003] [arXiv:1209.4049] [INSPIRE].
B. Hoare and A.A. Tseytlin, On string theory on AdS 3 × S 3 × T 4 with mixed 3-form flux: tree-level S-matrix, Nucl. Phys. B 873 (2013) 682 [arXiv:1303.1037] [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].
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].
A. Babichenko, A. Dekel and O. Ohlsson Sax, Finite-gap equations for strings on AdS 3 × S 3 × T 4 with mixed 3-form flux, arXiv:1405.6087 [INSPIRE].
N. Beisert, V. Dippel and M. Staudacher, A novel long range spin chain and planar N = 4 super Yang-Mills, JHEP 07 (2004) 075 [hep-th/0405001] [INSPIRE].
G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 01 (2007) P01021 [hep-th/0610251] [INSPIRE].
T. Klose, T. McLoughlin, R. Roiban and K. Zarembo, Worldsheet scattering in AdS 5 × S 5, JHEP 03 (2007) 094 [hep-th/0611169] [INSPIRE].
A. Rej, M. Staudacher and S. Zieme, Nesting and dressing, J. Stat. Mech. 08 (2007) P08006 [hep-th/0702151] [INSPIRE].
K. Sakai and Y. Satoh, Origin of dressing phase in N = 4 super Yang-Mills, Phys. Lett. B 661 (2008) 216 [hep-th/0703177] [INSPIRE].
N. Gromov and V. Kazakov, Asymptotic Bethe ansatz from string σ-model on S 3 × R, Nucl. Phys. B 780 (2007) 143 [hep-th/0605026] [INSPIRE].
N. Mann and J. Polchinski, Bethe ansatz for a quantum supercoset σ-model, Phys. Rev. D 72 (2005) 086002 [hep-th/0508232] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1407.7883
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Roiban, R., Sundin, P., Tseytlin, A. et al. The one-loop worldsheet S-matrix for the AdS n × S n × T 10−2n superstring. J. High Energ. Phys. 2014, 160 (2014). https://doi.org/10.1007/JHEP08(2014)160
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2014)160