Abstract
We study the finite size effect of rigidly rotating and spinning folded strings in (AdS3 × S3)ϰ background. We calculate the leading order exponential corrections to the infinite size dispersion relation of the giant magnon, and single spike solutions. For the spinning folded strings we write the finite size effect in terms of the known Lambert W -function.
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References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
J.A. Minahan and K. Zarembo, The Bethe ansatz for N = 4 super-Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].
N. Beisert and M. Staudacher, The N = 4 SYM integrable super spin chain, Nucl. Phys. B 670 (2003) 439 [hep-th/0307042] [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].
N. Beisert and M. Staudacher, Long-range P SU (2, 2|4) Bethe Ansatze for gauge theory and strings, Nucl. Phys. B 727 (2005) 1 [hep-th/0504190] [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].
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].
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].
J.A. Minahan, Circular semiclassical string solutions on AdS 5 × S 5, Nucl. Phys. B 648 (2003) 203 [hep-th/0209047] [INSPIRE].
A.A. Tseytlin, Semiclassical strings and AdS/CFT, hep-th/0409296 [INSPIRE].
D.M. Hofman and J.M. Maldacena, Giant magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].
N. Dorey, Magnon bound states and the AdS/CFT correspondence, J. Phys. A 39 (2006) 13119 [hep-th/0604175] [INSPIRE].
H.-Y. Chen, N. Dorey and K. Okamura, Dyonic giant magnons, JHEP 09 (2006) 024 [hep-th/0605155] [INSPIRE].
M. Kruczenski, J. Russo and A.A. Tseytlin, Spiky strings and giant magnons on S 5, JHEP 10 (2006) 002 [hep-th/0607044] [INSPIRE].
M. Kruczenski, Spiky strings and single trace operators in gauge theories, JHEP 08 (2005) 014 [hep-th/0410226] [INSPIRE].
R. Ishizeki and M. Kruczenski, Single spike solutions for strings on S 2 and S 3, Phys. Rev. D 76 (2007) 126006 [arXiv:0705.2429] [INSPIRE].
A.A. Tseytlin, Spinning strings and AdS/CFT duality, in From fields to strings. Volume 2, M. Shifman et al. eds., World Scientific, Singapore (2005), hep-th/0311139 [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].
C. Sieg and A. Torrielli, Wrapping interactions and the genus expansion of the 2-point function of composite operators, Nucl. Phys. B 723 (2005) 3 [hep-th/0505071] [INSPIRE].
J. Ambjørn, R.A. Janik and C. Kristjansen, Wrapping interactions and a new source of corrections to the spin-chain/string duality, Nucl. Phys. B 736 (2006) 288 [hep-th/0510171] [INSPIRE].
A.V. Kotikov et al., Dressing and wrapping, J. Stat. Mech. 0710 (2007) P10003 [arXiv:0704.3586] [INSPIRE].
G. Arutyunov, S. Frolov and M. Zamaklar, Finite-size effects from giant magnons, Nucl. Phys. B 778 (2007) 1 [hep-th/0606126] [INSPIRE].
D. Astolfi, V. Forini, G. Grignani and G.W. Semenoff, Gauge invariant finite size spectrum of the giant magnon, Phys. Lett. B 651 (2007) 329 [hep-th/0702043] [INSPIRE].
J.A. Minahan and O. Ohlsson Sax, Finite size effects for giant magnons on physical strings, Nucl. Phys. B 801 (2008) 97 [arXiv:0801.2064] [INSPIRE].
B. Ramadanovic and G.W. Semenoff, Finite size giant magnon, Phys. Rev. D 79 (2009) 126006 [arXiv:0803.4028] [INSPIRE].
T. Klose and T. McLoughlin, Interacting finite-size magnons, J. Phys. A 41 (2008) 285401 [arXiv:0803.2324] [INSPIRE].
I. Shenderovich, Giant magnons in AdS 4 /CF T 3 : Dispersion, quantization and finite-size corrections, arXiv:0807.2861 [INSPIRE].
C. Ahn and P. Bozhilov, Finite-size effects of Membranes on AdS 4 × S 7, JHEP 08 (2008) 054 [arXiv:0807.0566] [INSPIRE].
Y. Hatsuda and R. Suzuki, Finite-size effects for multi-magnon states, JHEP 09 (2008) 025 [arXiv:0807.0643] [INSPIRE].
C. Ahn and P. Bozhilov, Finite-size effects for single spike, JHEP 07 (2008) 105 [arXiv:0806.1085] [INSPIRE].
D.V. Bykov and S. Frolov, Giant magnons in TsT-transformed AdS 5 × S 5, JHEP 07 (2008) 071 [arXiv:0805.1070] [INSPIRE].
G. Grignani, T. Harmark, M. Orselli and G.W. Semenoff, Finite size giant magnons in the string dual of N = 6 superconformal Chern-Simons theory, JHEP 12 (2008) 008 [arXiv:0807.0205] [INSPIRE].
P. Bozhilov, Close to the giant magnons, arXiv:1010.5465 [INSPIRE].
C. Ahn and P. Bozhilov, Finite-size dyonic giant magnons in TsT-transformed AdS 5 × S 5, JHEP 07 (2010) 048 [arXiv:1005.2508] [INSPIRE].
S. Jain and K.L. Panigrahi, Spiky strings in AdS 4 × CP 3 with Neveu-Schwarz flux, JHEP 12 (2008) 064 [arXiv:0810.3516] [INSPIRE].
E. Floratos, G. Georgiou and G. Linardopoulos, Large-spin expansions of GKP strings, JHEP 03 (2014) 018 [arXiv:1311.5800] [INSPIRE].
E. Floratos and G. Linardopoulos, Large-spin and large-winding expansions of giant magnons and single spikes, Nucl. Phys. B 897 (2015) 229 [arXiv:1406.0796] [INSPIRE].
C. Ahn and P. Bozhilov, Finite-size giant magnons on η-deformed AdS 5 × S 5, Phys. Lett. B 737 (2014) 293 [arXiv:1406.0628] [INSPIRE].
C. Ahn and P. Bozhilov, String solutions in AdS 3 × S 3 × T 4 with NS-NS B-field, Phys. Rev. D 90 (2014) 066010 [arXiv:1404.7644] [INSPIRE].
C. Ahn, Finite-size effect of η-deformed AdS 5 × S 5 at strong coupling, Phys. Lett. B 767 (2017) 121 [arXiv:1611.09992] [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 AdS5 x S5, JHEP 04 (2014) 002 [arXiv:1312.3542] [INSPIRE].
T. Araujo et al., Yang-Baxter σ-models, conformal twists and noncommutative Yang-Mills theory, Phys. Rev. D 95 (2017) 105006 [arXiv:1702.02861] [INSPIRE].
T. Araujo et al., Conformal twists, Yang-Baxter σ-models & holographic noncommutativity, J. Phys. A 51 (2018) 235401 [arXiv:1705.02063] [INSPIRE].
T. Araujo et al., I in generalized supergravity, Eur. Phys. J. C 77 (2017) 739 [arXiv:1708.03163] [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].
D. Roychowdhury, Multispin magnons on deformed AdS 3 × S 3, Phys. Rev. D 95 (2017) 086009 [arXiv:1612.06217] [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].
S.P. Barik, K.L. Panigrahi and M. Samal, Spinning pulsating strings in (AdS 5 × S 5)ϰ, Eur. Phys. J. C 78 (2018) 280 [arXiv:1801.04248] [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].
M. Khouchen and J. Kluson, Giant magnon on deformed AdS 3 × S 3, Phys. Rev. D 90 (2014) 066001 [arXiv:1405.5017] [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].
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Panigrahi, K.L., Samal, M. Finite size effect from classical strings in deformed AdS3× S3. J. High Energ. Phys. 2018, 162 (2018). https://doi.org/10.1007/JHEP09(2018)162
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DOI: https://doi.org/10.1007/JHEP09(2018)162