Abstract
In this paper, considering the correspondence between spin chains and string sigma models, we explore the rotating string solutions over η deformed AdS5 × S5 in the so-called fast spinning limit. In our analysis, we focus only on the bosonic part of the full superstring action and compute the relevant limits on both (R × S3) η and (R × S5) η models. The resulting system reveals that in the fast spinning limit, the sigma model on η deformed S5 could be approximately thought of as the continuum limit of anisotropic SU(3) Heisenberg spin chain model. We compute the energy for a certain class of spinning strings in deformed S5 and we show that this energy can be mapped to that of a similar spinning string in the purely imaginary β deformed background.
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N. Beisert and P. Koroteev, Quantum deformations of the one-dimensional Hubbard model, J. Phys. A 41 (2008) 255204 [arXiv:0802.0777] [INSPIRE].
N. Beisert and F. Spill, The classical r-matrix of AdS/CFT and its Lie bialgebra structure, Commun. Math. Phys. 285 (2009) 537 [arXiv:0708.1762] [INSPIRE].
R. Murgan and R.I. Nepomechie, q-deformed SU(2|2) boundary S-matrices via the ZF algebra, JHEP 06 (2008) 096 [arXiv:0805.3142] [INSPIRE].
T. Mansson and K. Zoubos, Quantum symmetries and marginal deformations, JHEP 10 (2010) 043 [arXiv:0811.3755] [INSPIRE].
K. Zoubos, Review of AdS/CFT integrability, chapter IV.2: deformations, orbifolds and open boundaries, Lett. Math. Phys. 99 (2012) 375 [arXiv:1012.3998] [INSPIRE].
S.J. van Tongeren, Integrability of the AdS 5 × S 5 superstring and its deformations, J. Phys. A 47 (2014) 433001 [arXiv:1310.4854] [INSPIRE].
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].
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].
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].
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].
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, R. Borsato and S. Frolov, S-matrix for strings on η-deformed AdS 5 × S 5, JHEP 04 (2014) 002 [arXiv:1312.3542] [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 [Teor. Mat. Fiz. 182 (2014) 28] [arXiv:1403.6104] [INSPIRE].
G. Arutyunov, R. Borsato and S. Frolov, Puzzles of η-deformed AdS 5 × S 5, JHEP 12 (2015) 049 [arXiv:1507.04239] [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].
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].
I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS 5 × S 5 superstring, JHEP 04 (2014) 153 [arXiv:1401.4855] [INSPIRE].
I. Kawaguchi, T. Matsumoto and K. Yoshida, A Jordanian deformation of AdS space in type IIB supergravity, JHEP 06 (2014) 146 [arXiv:1402.6147] [INSPIRE].
M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, A new maximally supersymmetric background of IIB superstring theory, JHEP 01 (2002) 047 [hep-th/0110242] [INSPIRE].
R.R. Metsaev, Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background, Nucl. Phys. B 625 (2002) 70 [hep-th/0112044] [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Exactly solvable model of superstring in Ramond-Ramond plane wave background, Phys. Rev. D 65 (2002) 126004 [hep-th/0202109] [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].
C.G. Callan Jr., H.K. Lee, T. McLoughlin, J.H. Schwarz, I. Swanson and X. Wu, Quantizing string theory in AdS 5 × S 5 : beyond the pp wave, Nucl. Phys. B 673 (2003) 3 [hep-th/0307032] [INSPIRE].
C.G. Callan Jr., T. McLoughlin and I. Swanson, Holography beyond the Penrose limit, Nucl. Phys. B 694 (2004) 115 [hep-th/0404007] [INSPIRE].
S. Mizoguchi, T. Mogami and Y. Satoh, Penrose limits and Green-Schwarz strings, Class. Quant. Grav. 20 (2003) 1489 [hep-th/0209043] [INSPIRE].
L.A. Pando Zayas and J. Sonnenschein, On Penrose limits and gauge theories, JHEP 05 (2002) 010 [hep-th/0202186] [INSPIRE].
J.C. Plefka, Lectures on the plane wave string/gauge theory duality, Fortsch. Phys. 52 (2004) 264 [hep-th/0307101] [INSPIRE].
N. Beisert, S. Frolov, M. Staudacher and A.A. Tseytlin, Precision spectroscopy of AdS/CFT, JHEP 10 (2003) 037 [hep-th/0308117] [INSPIRE].
G. Arutyunov, S. Frolov, J. Russo and A.A. Tseytlin, Spinning strings in AdS 5 × S 5 and integrable systems, Nucl. Phys. B 671 (2003) 3 [hep-th/0307191] [INSPIRE].
M. Kruczenski, Spin chains and string theory, Phys. Rev. Lett. 93 (2004) 161602 [hep-th/0311203] [INSPIRE].
G. Arutyunov, J. Russo and A.A. Tseytlin, Spinning strings in AdS 5 × S 5 : new integrable system relations, Phys. Rev. D 69 (2004) 086009 [hep-th/0311004] [INSPIRE].
M. Kruczenski, A.V. Ryzhov and A.A. Tseytlin, Large spin limit of AdS 5 × S 5 string theory and low-energy expansion of ferromagnetic spin chains, Nucl. Phys. B 692 (2004) 3 [hep-th/0403120] [INSPIRE].
R. Hernandez and E. Lopez, The SU(3) spin chain σ-model and string theory, JHEP 04 (2004) 052 [hep-th/0403139] [INSPIRE].
B. Stefanski, Jr. and A.A. Tseytlin, Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations, JHEP 05 (2004) 042 [hep-th/0404133] [INSPIRE].
J.A. Minahan, A. Tirziu and A.A. Tseytlin, 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model, Nucl. Phys. B 735 (2006) 127 [hep-th/0509071] [INSPIRE].
J.A. Minahan, A. Tirziu and A.A. Tseytlin, 1/J 2 corrections to BMN energies from the quantum long range Landau-Lifshitz model, JHEP 11 (2005) 031 [hep-th/0510080] [INSPIRE].
V.A. Kazakov, A. Marshakov, J.A. Minahan and K. Zarembo, Classical/quantum integrability in AdS/CFT, JHEP 05 (2004) 024 [hep-th/0402207] [INSPIRE].
S.A. Frolov, R. Roiban and A.A. Tseytlin, Gauge-string duality for superconformal deformations of N = 4 super Yang-Mills theory, JHEP 07 (2005) 045 [hep-th/0503192] [INSPIRE].
W.-Y. Wen, Spin chain from marginally deformed AdS 3 × S 3, Phys. Rev. D 75 (2007) 067901 [hep-th/0610147] [INSPIRE].
H. Dimov and R.C. Rashkov, A note on spin chain/string duality, Int. J. Mod. Phys. A 20 (2005) 4337 [hep-th/0403121] [INSPIRE].
S. Bellucci, P.Y. Casteill, J.F. Morales and C. Sochichiu, SL(2) spin chain and spinning strings on AdS 5 × S 5, Nucl. Phys. B 707 (2005) 303 [hep-th/0409086] [INSPIRE].
W.-H. Huang, Spin chain with magnetic field and spinning string in magnetic field background, Phys. Rev. D 74 (2006) 027901 [hep-th/0605242] [INSPIRE].
N. Dorey, A spin chain from string theory, Acta Phys. Polon. B 39 (2008) 3081 [arXiv:0805.4387] [INSPIRE].
T. Kameyama and K. Yoshida, Anisotropic Landau-Lifshitz σ-models from q-deformed AdS 5 × S 5 superstrings, JHEP 08 (2014) 110 [arXiv:1405.4467] [INSPIRE].
G. Arutyunov and D. Medina-Rincon, Deformed Neumann model from spinning strings on (AdS 5 × S 5) η , JHEP 10 (2014) 050 [arXiv:1406.2536] [INSPIRE].
G. Arutyunov, M. Heinze and D. Medina-Rincon, Integrability of the η-deformed Neumann-Rosochatius model, J. Phys. A 50 (2017) 035401 [arXiv:1607.05190] [INSPIRE].
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].
R. Hernandez and J.M. Nieto, Spinning strings in the η-deformed Neumann-Rosochatius system, Phys. Rev. D 96 (2017) 086010 [arXiv:1707.08032] [INSPIRE].
T. Kameyama and K. Yoshida, String theories on warped AdS backgrounds and integrable deformations of spin chains, JHEP 05 (2013) 146 [arXiv:1304.1286] [INSPIRE].
S.A. Frolov, R. Roiban and A.A. Tseytlin, Gauge-string duality for (non)supersymmetric deformations of N = 4 super Yang-Mills theory, Nucl. Phys. B 731 (2005) 1 [hep-th/0507021] [INSPIRE].
O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [INSPIRE].
S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [INSPIRE].
A.M. Perelomov, Generalized coherent states and their applications, Springer, Berlin Germany, (1986) [INSPIRE].
S. Ryang, Circular and folded multi-spin strings in spin chain σ-models, JHEP 10 (2004) 059 [hep-th/0409217] [INSPIRE].
J. Lamers, A pedagogical introduction to quantum integrability, with a view towards theoretical high-energy physics, PoS(Modave2014)001 [arXiv:1501.06805] [INSPIRE].
C. Kristjansen, Three spin strings on AdS 5 × S 5 from N = 4 SYM, Phys. Lett. B 586 (2004) 106 [hep-th/0402033] [INSPIRE].
C. Kristjansen and T. Mansson, The circular, elliptic three spin string from the SU(3) spin chain, Phys. Lett. B 596 (2004) 265 [hep-th/0406176] [INSPIRE].
L. Freyhult and C. Kristjansen, Rational three-spin string duals and non-anomalous finite size effects, JHEP 05 (2005) 043 [hep-th/0502122] [INSPIRE].
V.A. Fateev, The σ-model (dual) representation for a two-parameter family of integrable quantum field theories, Nucl. Phys. B 473 (1996) 509 [INSPIRE].
R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N = 1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95[hep-th/9503121] [INSPIRE].
D. Bundzik and T. Mansson, The general Leigh-Strassler deformation and integrability, JHEP 01 (2006) 116 [hep-th/0512093] [INSPIRE].
T. Matsumoto and K. Yoshida, Lunin-Maldacena backgrounds from the classical Yang-Baxter equation — towards the gravity/CYBE correspondence, JHEP 06 (2014) 135 [arXiv:1404.1838] [INSPIRE].
V.G.M. Puletti and T. Mansson, The dual string σ-model of the SU q (3) sector, JHEP 01 (2012) 129 [arXiv:1106.1116] [INSPIRE].
T. Mansson, The Leigh-Strassler deformation and the quest for integrability, JHEP 06 (2007) 010 [hep-th/0703150] [INSPIRE].
D. Giataganas, L.A. Pando Zayas and K. Zoubos, On marginal deformations and non-integrability, JHEP 01 (2014) 129 [arXiv:1311.3241] [INSPIRE].
D. Roychowdhury, Analytic integrability for strings on η and λ deformed backgrounds, JHEP 10 (2017) 056 [arXiv:1707.07172] [INSPIRE].
R. Hernandez and E. Lopez, Spin chain σ-models with fermions, JHEP 11 (2004) 079 [hep-th/0410022] [INSPIRE].
B. Stefanski, Jr. and A.A. Tseytlin, Super spin chain coherent state actions and AdS 5 × S 5 superstring, Nucl. Phys. B 718 (2005) 83 [hep-th/0503185] [INSPIRE].
B. Stefanski, Jr., Landau-Lifshitz σ-models, fermions and the AdS/CFT correspondence, JHEP 07 (2007) 009 [arXiv:0704.1460] [INSPIRE].
D. Arnaudon, Algebraic approach to q-deformed supersymmetric variants of the Hubbard model with pair hoppings, JHEP 12 (1997) 006 [physics/9711001] [INSPIRE].
V.V. Bazhanov and Z. Tsuboi, Baxter’s Q-operators for supersymmetric spin chains, Nucl. Phys. B 805 (2008) 451 [arXiv:0805.4274] [INSPIRE].
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Banerjee, A., Bhattacharyya, A. & Roychowdhury, D. Fast spinning strings on η deformed AdS5 × S5. J. High Energ. Phys. 2018, 35 (2018). https://doi.org/10.1007/JHEP02(2018)035
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DOI: https://doi.org/10.1007/JHEP02(2018)035