Abstract
We initiate the perturbative study of the S-matrix for the excitations on top of the GKP vacuum at strong coupling. Using the string sigma model action expanded around the null cusp classical solution, we compute the tree-level S-matrix elements and compare them with the predictions from the asymptotic Bethe Ansatz. We also check the factorization of the three-body S-matrix for various bosonic processes, finding precise agreement with the constraints imposed by integrability.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for \( \mathcal{N}=4 \) super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].
N. Beisert and M. Staudacher, The \( \mathcal{N}=4 \) SYM integrable super spin chain, Nucl. Phys. B 670 (2003) 439 [hep-th/0307042] [INSPIRE].
N. Beisert and M. Staudacher, Long-range PSU(2, 2|4) Bethe Ansatze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, A Semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
S. Frolov and A.A. Tseytlin, Semiclassical quantization of rotating superstring in AdS5 × S5, JHEP 06 (2002) 007 [hep-th/0204226] [INSPIRE].
R.R. Metsaev, C.B. Thorn and A.A. Tseytlin, Light cone superstring in AdSspace-time, Nucl. Phys. B 596 (2001) 151 [hep-th/0009171] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Superstring action in AdS5 × S5 . κ-symmetry light cone gauge, Phys. Rev. D 63 (2001) 046002 [hep-th/0007036] [INSPIRE].
S. Giombi, R. Ricci, R. Roiban, A.A. Tseytlin and C. Vergu, Quantum AdS 5 × S5 superstring in the AdSlight-cone gauge, JHEP 03 (2010) 003 [arXiv:0912.5105] [INSPIRE].
L.F. Alday and J.M. Maldacena, Comments on operators with large spin, JHEP 11 (2007) 019 [arXiv:0708.0672] [INSPIRE].
B. Basso, G.P. Korchemsky and J. Kotanski, Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. Lett. 100 (2008) 091601 [arXiv:0708.3933] [INSPIRE].
R. Roiban, A. Tirziu and A.A. Tseytlin, Two-loop world-sheet corrections in AdS5 × S5 superstring, JHEP 07 (2007) 056 [arXiv:0704.3638] [INSPIRE].
R. Roiban and A.A. Tseytlin, Strong-coupling expansion of cusp anomaly from quantum superstring, JHEP 11 (2007) 016 [arXiv:0709.0681] [INSPIRE].
R. Roiban and A.A. Tseytlin, Spinning superstrings at two loops: Strong-coupling corrections to dimensions of large-twist SYM operators, Phys. Rev. D 77 (2008) 066006 [arXiv:0712.2479] [INSPIRE].
K. Zarembo and S. Zieme, Fine Structure of String Spectrum in AdS5 × S5, JETP Lett. 95 (2012) 219 [arXiv:1110.6146] [INSPIRE].
N. Gromov and P. Vieira, The all loop AdS4 /CFT3 Bethe ansatz, JHEP 01 (2009) 016 [arXiv:0807.0777] [INSPIRE].
B. Basso and A. Rej, Bethe ansätze for GKP strings, Nucl. Phys. B 879 (2014) 162 [arXiv:1306.1741] [INSPIRE].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, \( \mathcal{N}=6 \) superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [INSPIRE].
D.V. Uvarov, \( {\mathrm{AdS}}_4\times \mathrm{\mathbb{C}}{\mathrm{\mathbb{P}}}^3 \) superstring in the light-cone gauge, Nucl. Phys. B 826 (2010) 294 [arXiv:0906.4699] [INSPIRE].
D.V. Uvarov, Light-cone gauge Hamiltonian for \( {\mathrm{AdS}}_4\times \mathrm{\mathbb{C}}{\mathrm{\mathbb{P}}}^3 \) superstring, Mod. Phys. Lett. A 25 (2010) 1251 [arXiv:0912.1044] [INSPIRE].
D. Uvarov, Light-cone gauge formulation for \( {\mathrm{AdS}}_4\times \mathrm{\mathbb{C}}{\mathrm{\mathbb{P}}}^3 \) superstring, Phys. Part. Nucl. Lett. 8 (2011) 272.
L. Bianchi, M.S. Bianchi, A. Bres, V. Forini and E. Vescovi, Two-loop cusp anomaly in ABJM at strong coupling, JHEP 10 (2014) 13 [arXiv:1407.4788] [INSPIRE].
L. Bianchi and M.S. Bianchi, Quantum dispersion relations for the \( {\mathrm{AdS}}_4\times \mathrm{\mathbb{C}}{\mathrm{\mathbb{P}}}^3 \) GKP string, JHEP 11 (2015) 031 [arXiv:1505.00783] [INSPIRE].
D. Fioravanti, S. Piscaglia and M. Rossi, On the scattering over the GKP vacuum, Phys. Lett. B 728 (2014) 288 [arXiv:1306.2292] [INSPIRE].
D. Fioravanti, S. Piscaglia and M. Rossi, Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops, Nucl. Phys. B 898 (2015) 301 [arXiv:1503.08795] [INSPIRE].
L.F. Alday, D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, An Operator Product Expansion for Polygonal null Wilson Loops, JHEP 04 (2011) 088 [arXiv:1006.2788] [INSPIRE].
D. Gaiotto, J. Maldacena, A. Sever and P. Vieira, Pulling the straps of polygons, JHEP 12 (2011) 011 [arXiv:1102.0062] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for \( \mathcal{N}=4 \) Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 111 (2013) 091602 [arXiv:1303.1396] [INSPIRE].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes, Nucl. Phys. B 826 (2010) 337 [arXiv:0712.1223] [INSPIRE].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, On planar gluon amplitudes/Wilson loops duality, Nucl. Phys. B 795 (2008) 52 [arXiv:0709.2368] [INSPIRE].
A. Brandhuber, P. Heslop and G. Travaglini, MHV amplitudes in \( \mathcal{N}=4 \) super Yang-Mills and Wilson loops, Nucl. Phys. B 794 (2008) 231 [arXiv:0707.1153] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data, JHEP 01 (2014) 008 [arXiv:1306.2058] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions, JHEP 08 (2014) 085 [arXiv:1402.3307] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Collinear Limit of Scattering Amplitudes at Strong Coupling, Phys. Rev. Lett. 113 (2014) 261604 [arXiv:1405.6350] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion, JHEP 09 (2014) 149 [arXiv:1407.1736] [INSPIRE].
B. Basso, J. Caetano, L. Cordova, A. Sever and P. Vieira, OPE for all Helicity Amplitudes, JHEP 08 (2015) 018 [arXiv:1412.1132] [INSPIRE].
B. Basso, J. Caetano, L. Cordova, A. Sever and P. Vieira, OPE for all Helicity Amplitudes II. Form Factors and Data analysis, arXiv:1508.02987 [INSPIRE].
B. Basso, A. Sever and P. Vieira, Hexagonal Wilson Loops in Planar \( \mathcal{N}=4 \) SYM Theory at Finite Coupling, arXiv:1508.03045 [INSPIRE].
S. Giombi, R. Ricci, R. Roiban and A.A. Tseytlin, Quantum dispersion relations for excitations of long folded spinning superstring in AdS5 × S5, JHEP 01 (2011) 128 [arXiv:1011.2755] [INSPIRE].
T. Klose, T. McLoughlin, J.A. Minahan and K. Zarembo, World-sheet scattering in AdS5 × S5 at two loops, JHEP 08 (2007) 051 [arXiv:0704.3891] [INSPIRE].
A. Zamolodchikov, Ising Spectroscopy II: Particles and poles at T > T c , arXiv:1310.4821 [INSPIRE].
B. Berg, M. Karowski, P. Weisz and V. Kurak, Factorized U(n) Symmetric S-Matrices in Two-Dimensions, Nucl. Phys. B 134 (1978) 125 [INSPIRE].
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].
O.T. Engelund, R.W. McKeown and R. Roiban, Generalized unitarity and the worldsheet S-matrix in AdS n × Sn × M10−2n, JHEP 08 (2013) 023 [arXiv:1304.4281] [INSPIRE].
L. Bianchi, V. Forini and B. Hoare, Two-dimensional S-matrices from unitarity cuts, JHEP 07 (2013) 088 [arXiv:1304.1798] [INSPIRE].
L. Bianchi and B. Hoare, AdS3 × S3 × M4 string S-matrices from unitarity cuts, JHEP 08 (2014) 097 [arXiv:1405.7947] [INSPIRE].
O.T. Engelund and R. Roiban, On the asymptotic states and the quantum S-matrix of the η-deformed AdS5 × S5 superstring, JHEP 03 (2015) 168 [arXiv:1412.5256] [INSPIRE].
B. Hoare, A. Pittelli and A. Torrielli, Integrable S-matrices, massive and massless modes and the AdS2 × S2 superstring, JHEP 11 (2014) 051 [arXiv:1407.0303] [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: 1508.07331
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
Bianchi, L., Bianchi, M.S. Worldsheet scattering for the GKP string. J. High Energ. Phys. 2015, 178 (2015). https://doi.org/10.1007/JHEP11(2015)178
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)178