Abstract
We derive the part of the Lagrangian for the sigma model on the η-deformed AdS5 × S5 space which is quadratic in fermions and has the full dependence on bosons. We then show that there exists a field redefinition which brings the corresponding La-grangian to the standard form of type IIB Green-Schwarz superstring. Reading off the corresponding RR couplings, we observe that they fail to satisfy the supergravity equations of motion, despite the presence of κ-symmetry. However, in a special scaling limit our solution reproduces the supergravity background found by Maldacena and Russo. Further, using the fermionic Lagrangian, we compute a number of new matrix elements of the tree level world-sheet scattering matrix. We then show that after a unitary transformation on the basis of two-particle states which is not one-particle factorisable, the corresponding T-matrix factorises into two equivalent parts. Each part satisfies the classical Yang-Baxter equation and coincides with the large tension limit of the q-deformed S-matrix.
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F. Delduc, M. Magro and B. Vicedo, An integrable deformation of the AdS 5 × S 5 superstring action, Phys. Rev. Lett. 112 (2014) 051601 [arXiv:1309.5850] [INSPIRE].
C. Klimčík, Yang-Baxter σ-models and dS/AdS T duality, JHEP 12 (2002) 051 [hep-th/0210095] [INSPIRE].
C. Klimčík, On integrability of the Yang-Baxter σ-model, J. Math. Phys. 50 (2009) 043508 [arXiv:0802.3518] [INSPIRE].
G. Arutyunov, R. Borsato and S. Frolov, S-matrix for strings on η-deformed AdS 5 × S 5, JHEP 04 (2014) 002 [arXiv:1312.3542] [INSPIRE].
B. Hoare, R. Roiban and A.A. Tseytlin, On deformations of AdS n × S n supercosets, JHEP 06 (2014) 002 [arXiv:1403.5517] [INSPIRE].
G. Arutyunov, M. de Leeuw and S.J. van Tongeren, The exact spectrum and mirror duality of the (AdS 5 × S 5) η superstring, Theor. Math. Phys. 182 (2015) 23 [arXiv:1403.6104] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, Derivation of the action and symmetries of the q-deformed AdS 5 × S 5 superstring, JHEP 10 (2014) 132 [arXiv:1406.6286] [INSPIRE].
O. Lunin, R. Roiban and A.A. Tseytlin, Supergravity backgrounds for deformations of AdS n × S n supercoset string models, Nucl. Phys. B 891 (2015) 106 [arXiv:1411.1066] [INSPIRE].
O.T. Engelund and R. Roiban, On the asymptotic states and the quantum S matrix of the η-deformed AdS 5 × S 5 superstring, JHEP 03 (2015) 168 [arXiv:1412.5256] [INSPIRE].
K. Sfetsos, Integrable interpolations: From exact CFTs to non-Abelian T-duals, Nucl. Phys. B 880 (2014) 225 [arXiv:1312.4560] [INSPIRE].
T.J. Hollowood, J.L. Miramontes and D.M. Schmidtt, An Integrable Deformation of the AdS 5 × S 5 Superstring, J. Phys. A 47 (2014) 495402 [arXiv:1409.1538] [INSPIRE].
K. Sfetsos and D.C. Thompson, Spacetimes for λ-deformations, JHEP 12 (2014) 164 [arXiv:1410.1886] [INSPIRE].
S. Demulder, K. Sfetsos and D.C. Thompson, Integrable λ-deformations: Squashing Coset CFTs and AdS 5 × S 5, JHEP 07 (2015) 019 [arXiv:1504.02781] [INSPIRE].
I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS 5 × S 5 superstring, JHEP 04 (2014) 153 [arXiv:1401.4855] [INSPIRE].
T. Matsumoto and K. Yoshida, Integrability of classical strings dual for noncommutative gauge theories, JHEP 06 (2014) 163 [arXiv:1404.3657] [INSPIRE].
T. Matsumoto and K. Yoshida, Integrable deformations of the AdS 5 × S 5 superstring and the classical Yang-Baxter equation — Towards the gravity/CYBE correspondence —, J. Phys. Conf. Ser. 563 (2014) 012020 [arXiv:1410.0575] [INSPIRE].
T. Matsumoto and K. Yoshida, Yang-Baxter deformations and string dualities, JHEP 03 (2015) 137 [arXiv:1412.3658] [INSPIRE].
T. Matsumoto and K. Yoshida, Yang-Baxter σ-models based on the CYBE, Nucl. Phys. B 893 (2015) 287 [arXiv:1501.03665] [INSPIRE].
S.J. van Tongeren, On classical Yang-Baxter based deformations of the AdS 5 × S 5 superstring, JHEP 06 (2015) 048 [arXiv:1504.05516] [INSPIRE].
S.J. van Tongeren, Yang-Baxter deformations, AdS/CFT and twist-noncommutative gauge theory, arXiv:1506.01023 [INSPIRE].
N. Beisert and P. Koroteev, Quantum Deformations of the One-Dimensional Hubbard Model, J. Phys. A 41 (2008) 255204 [arXiv:0802.0777] [INSPIRE].
B. Hoare, T.J. Hollowood and J.L. Miramontes, q-Deformation of the AdS 5 × S 5 Superstring S-matrix and its Relativistic Limit, JHEP 03 (2012) 015 [arXiv:1112.4485] [INSPIRE].
A.A. Tseytlin, On dilaton dependence of type-II superstring action, Class. Quant. Grav. 13 (1996) L81 [hep-th/9601109] [INSPIRE].
M. Cvetič, H. Lü, C.N. Pope and K.S. Stelle, T duality in the Green-Schwarz formalism and the massless/massive IIA duality map, Nucl. Phys. B 573 (2000) 149 [hep-th/9907202] [INSPIRE].
L. Wulff, The type-II superstring to order θ 4, JHEP 07 (2013) 123 [arXiv:1304.6422] [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].
G. Arutyunov and S.J. van Tongeren, Double Wick rotating Green-Schwarz strings, JHEP 05 (2015) 027 [arXiv:1412.5137] [INSPIRE].
G. Arutyunov and S.J. van Tongeren, AdS5 × S5 mirror model as a string σ-model, Phys. Rev. Lett. 113 (2014) 261605 [arXiv:1406.2304] [INSPIRE].
S. Frolov, Comments on the AdS5 × S5 superstring, talk at the workshop Supersymmetric Field Theories, Nordita, Stockholm Sweden (2014), http://agenda.albanova.se/getFile.py/access?resId=258&materialId=slides&confId=4134.
J.M. Maldacena and J.G. Russo, Large-N limit of noncommutative gauge theories, JHEP 09 (1999) 025 [hep-th/9908134] [INSPIRE].
M.T. Grisaru, P.S. Howe, L. Mezincescu, B. Nilsson and P.K. Townsend, N = 2 Superstrings in a Supergravity Background, Phys. Lett. B 162 (1985) 116 [INSPIRE].
E. Bergshoeff, E. Sezgin and P.K. Townsend, Superstring Actions in D = 3, 4, 6, 10 Curved Superspace, Phys. Lett. B 169 (1986) 191 [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].
T. Klose, T. McLoughlin, R. Roiban and K. Zarembo, Worldsheet scattering in AdS5 × S5, JHEP 03 (2007) 094 [hep-th/0611169] [INSPIRE].
G. Arutyunov and D. Medina-Rincon, Deformed Neumann model from spinning strings on (AdS 5 × S 5) η , JHEP 10 (2014) 50 [arXiv:1406.2536] [INSPIRE].
S. Frolov and R. Roiban, η-deformed AdS5 × S5, presented by S. Frolov at the workshop Integrability in Gauge and String Theory, Hamburg Germany (2014).
T. Kameyama and K. Yoshida, A new coordinate system for q-deformed AdS 5 × S 5 and classical string solutions, J. Phys. A 48 (2015) 075401 [arXiv:1408.2189] [INSPIRE].
A. Banerjee and K.L. Panigrahi, On the rotating and oscillating strings in (AdS 3 × S 3) κ , JHEP 09 (2014) 048 [arXiv:1406.3642] [INSPIRE].
M. Khouchen and J. Kluson, Giant Magnon on Deformed AdS 3 × S 3, Phys. Rev. D 90 (2014) 066001 [arXiv:1405.5017] [INSPIRE].
K.L. Panigrahi, P.M. Pradhan and M. Samal, Pulsating strings on (AdS 3 × S 3) κ , JHEP 03 (2015) 010 [arXiv:1412.6936] [INSPIRE].
P. Bozhilov, Some three-point correlation functions in the eta-deformed AdS 5 × S 5, arXiv:1502.00610 [INSPIRE].
A. Banerjee, S. Bhattacharya and K.L. Panigrahi, Spiky strings in κ-deformed AdS, JHEP 06 (2015) 057 [arXiv:1503.07447] [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].
B. Vicedo, Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles, J. Phys. A 48 (2015) 355203 [arXiv:1504.06303] [INSPIRE].
B. Hoare and A.A. Tseytlin, On integrable deformations of superstring σ-models related to AdS n × S n supercosets, Nucl. Phys. B 897 (2015) 448 [arXiv:1504.07213] [INSPIRE].
K. Sfetsos, K. Siampos and D.C. Thompson, Generalised integrable λ- and η-deformations and their relation, Nucl. Phys. B 899 (2015) 489 [arXiv:1506.05784] [INSPIRE].
D.Z. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).
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ArXiv ePrint: 1507.04239
Correspondent fellow at Steklov Mathematical Institute, Moscow. (Gleb Arutyunov and Sergey Frolov)
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Arutyunov, G., Borsato, R. & Frolov, S. Puzzles of η-deformed AdS5 × S5 . J. High Energ. Phys. 2015, 1–60 (2015). https://doi.org/10.1007/JHEP12(2015)049
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DOI: https://doi.org/10.1007/JHEP12(2015)049