Abstract
We consider the three-parameter integrable deformation of the AdS3 × S3 superstring background constructed in arXiv:1811.00453. Working on the string worldsheet in uniform lightcone gauge, we find the tree-level bosonic S matrix of the model and study some of its limits.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Arutyunov and S. Frolov, Foundations of the AdS5 × S5 Superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
D. Bombardelli et al., An integrability primer for the gauge-gravity correspondence: An introduction, J. Phys. A 49 (2016) 320301 [arXiv:1606.02945] [INSPIRE].
A. Sfondrini, Towards integrability for AdS3/CFT2, J. Phys. A 48 (2015) 023001 [arXiv:1406.2971] [INSPIRE].
A. Babichenko, B. Stefański Jr. and K. Zarembo, Integrability and the AdS3/CFT2 correspondence, JHEP 03 (2010) 058 [arXiv:0912.1723] [INSPIRE].
P. Sundin and L. Wulff, Classical integrability and quantum aspects of the AdS3 × S3 × S3 × S1 superstring, JHEP 10 (2012) 109 [arXiv:1207.5531] [INSPIRE].
R. Borsato, O. Ohlsson Sax and A. Sfondrini, A dynamic \( \mathfrak{su} \)(1|1)2 S-matrix for AdS3/CFT2, JHEP 04 (2013) 113 [arXiv:1211.5119] [INSPIRE].
R. Borsato, O. Ohlsson Sax and A. Sfondrini, All-loop Bethe ansatz equations for AdS3/CFT2, JHEP 04 (2013) 116 [arXiv:1212.0505] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański, The AdS3 × S3 × S3 × S1 worldsheet S matrix, J. Phys. A 48 (2015) 415401 [arXiv:1506.00218] [INSPIRE].
A. Dei and A. Sfondrini, Integrable S matrix, mirror TBA and spectrum for the stringy AdS3 × S3 × S3 × S1 WZW model, JHEP 02 (2019) 072 [arXiv:1812.08195] [INSPIRE].
A. Cagnazzo and K. Zarembo, B-field in AdS3/CFT2 Correspondence and Integrability, JHEP 11 (2012) 133 [Erratum ibid. 04 (2013) 003] [arXiv:1209.4049] [INSPIRE].
M. Beccaria, F. Levkovich-Maslyuk, G. Macorini and A.A. Tseytlin, Quantum corrections to spinning superstrings in AdS3 × S3 × M4: determining the dressing phase, JHEP 04 (2013) 006 [arXiv:1211.6090] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefański and A. Torrielli, The al l-loop integrable spin-chain for strings on AdS3 × S3 × T4: the massive sector, JHEP 08 (2013) 043 [arXiv:1303.5995] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefański Jr. and A. Torrielli, Dressing phases of AdS3/CFT2, Phys. Rev. D 88 (2013) 066004 [arXiv:1306.2512] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and SL(2, ℝ) WZW model 1.: The Spectrum, J. Math. Phys. 42 (2001) 2929 [hep-th/0001053] [INSPIRE].
J.M. Maldacena, H. Ooguri and J. Son, Strings in AdS3 and the SL(2, ℝ) WZW model. Part 2. Euclidean black hole, J. Math. Phys. 42 (2001) 2961 [hep-th/0005183] [INSPIRE].
J.M. Maldacena and H. Ooguri, Strings in AdS3 and the SL(2, ℝ) WZW model. Part 3. Correlation functions, Phys. Rev. D 65 (2002) 106006 [hep-th/0111180] [INSPIRE].
M. Baggio and A. Sfondrini, Strings on NS-NS Backgrounds as Integrable Deformations, Phys. Rev. D 98 (2018) 021902 [arXiv:1804.01998] [INSPIRE].
A. Dei and A. Sfondrini, Integrable spin chain for stringy Wess-Zumino-Witten models, JHEP 07 (2018) 109 [arXiv:1806.00422] [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].
S.L. Lukyanov, The integrable harmonic map problem versus Ricci flow, Nucl. Phys. B 865 (2012) 308 [arXiv:1205.3201] [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].
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].
S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [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].
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 AdS5 × S5 superstring, JHEP 06 (2015) 048 [arXiv:1504.05516] [INSPIRE].
D. Osten and S.J. van Tongeren, Abelian Yang-Baxter deformations and TsT transformations, Nucl. Phys. B 915 (2017) 184 [arXiv:1608.08504] [INSPIRE].
R. Borsato and L. Wulff, Integrable Deformations of T-Dual σ Models, Phys. Rev. Lett. 117 (2016) 251602 [arXiv:1609.09834] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, On classical q-deformations of integrable σ-models, JHEP 11 (2013) 192 [arXiv:1308.3581] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, An integrable deformation of the AdS5 × S5 superstring action, Phys. Rev. Lett. 112 (2014) 051601 [arXiv:1309.5850] [INSPIRE].
I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS5 × S5 superstring, JHEP 04 (2014) 153 [arXiv:1401.4855] [INSPIRE].
B. Hoare, R. Roiban and A.A. Tseytlin, On deformations of AdSn × Sn supercosets, JHEP 06 (2014) 002 [arXiv:1403.5517] [INSPIRE].
C. Klimčík, Integrability of the bi-Yang-Baxter σ-model, Lett. Math. Phys. 104 (2014) 1095 [arXiv:1402.2105] [INSPIRE].
B. Hoare, Towards a two-parameter q-deformation of AdS3 × S3 × M4 superstrings, Nucl. Phys. B 891 (2015) 259 [arXiv:1411.1266] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, Integrable double deformation of the principal chiral model, Nucl. Phys. B 891 (2015) 312 [arXiv:1410.8066] [INSPIRE].
F. Delduc, B. Hoare, T. Kameyama, S. Lacroix and M. Magro, Three-parameter integrable deformation of ℤ4 permutation supercosets, JHEP 01 (2019) 109 [arXiv:1811.00453] [INSPIRE].
G. Arutyunov, R. Borsato and S. Frolov, Puzzles of η-deformed AdS5 × S5, JHEP 12 (2015) 049 [arXiv:1507.04239] [INSPIRE].
R. Borsato and L. Wulff, Target space supergeometry of η and λ-deformed strings, JHEP 10 (2016) 045 [arXiv:1608.03570] [INSPIRE].
B. Hoare and F.K. Seibold, Supergravity backgrounds of the η-deformed AdS2 × S2 × T6 and AdS5 × S5 superstrings, JHEP 01 (2019) 125 [arXiv:1811.07841] [INSPIRE].
F.K. Seibold, Two-parameter integrable deformations of the AdS3 × S3 × T4 superstring, JHEP 10 (2019) 049 [arXiv:1907.05430] [INSPIRE].
G. Arutyunov and S. Frolov, Integrable Hamiltonian for classical strings on AdS5 × S5, JHEP 02 (2005) 059 [hep-th/0411089] [INSPIRE].
G. Arutyunov and S. Frolov, Uniform light-cone gauge for strings in AdS5 × S5: Solving SU(1|1) sector, JHEP 01 (2006) 055 [hep-th/0510208] [INSPIRE].
G. Arutyunov, S. Frolov and M. Zamaklar, Finite-size Effects from Giant Magnons, Nucl. Phys. B 778 (2007) 1 [hep-th/0606126] [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].
G. Arutyunov, S. Frolov, J. Plefka and M. Zamaklar, The Off-shell Symmetry Algebra of the Light-cone AdS5 × S5 Superstring, J. Phys. A 40 (2007) 3583 [hep-th/0609157] [INSPIRE].
G. Arutyunov, S. Frolov and M. Zamaklar, The Zamolodchikov-Faddeev algebra for AdS5 × S5 superstring, JHEP 04 (2007) 002 [hep-th/0612229] [INSPIRE].
N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefanski, Towards the All-Loop Worldsheet S Matrix for AdS3 × S3 × T4, Phys. Rev. Lett. 113 (2014) 131601 [arXiv:1403.4543] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefanski, The complete AdS3 × S3 × T4 worldsheet S matrix, JHEP 10 (2014) 066 [arXiv:1406.0453] [INSPIRE].
F. Delduc, M. Magro and B. Vicedo, Derivation of the action and symmetries of the q-deformed AdS5 × S5 superstring, JHEP 10 (2014) 132 [arXiv:1406.6286] [INSPIRE].
N. Beisert and P. Koroteev, Quantum Deformations of the One-Dimensional Hubbard Model, J. Phys. A 41 (2008) 255204 [arXiv:0802.0777] [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].
F.K. Seibold, S.J. van Tongeren and Y. Zimmermann, The twisted story of worldsheet scattering in η-deformed AdS5 × S5, arXiv:2007.09136 [INSPIRE].
A.B. Zamolodchikov, Thermodynamic Bethe Ansatz in Relativistic Models. Scaling Three State Potts and Lee-yang Models, Nucl. Phys. B 342 (1990) 695 [INSPIRE].
T. Lloyd, O. Ohlsson Sax, A. Sfondrini and J. Stefański, Bogdan, The complete worldsheet S matrix of superstrings on AdS3 × S3 × T4 with mixed three-form flux, Nucl. Phys. B 891 (2015) 570 [arXiv:1410.0866] [INSPIRE].
S. Frolov, \( T\overline{T} \) Deformation and the Light-Cone Gauge, Proc. Steklov Inst. Math. 309 (2020) 107 [arXiv:1905.07946] [INSPIRE].
S. Frolov, \( T\overline{T} \), \( \tilde{J}J \), JT and \( \tilde{J}T \) deformations, J. Phys. A 53 (2020) 025401 [arXiv:1907.12117] [INSPIRE].
A. Sfondrini and S.J. van Tongeren, \( T\overline{T} \) deformations as TsT transformations, Phys. Rev. D 101 (2020) 066022 [arXiv:1908.09299] [INSPIRE].
D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from N = 4 superYang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
P. Sundin and L. Wulff, The complete one-loop BMN S-matrix in AdS3 × S3 × T4, JHEP 06 (2016) 062 [arXiv:1605.01632] [INSPIRE].
B. Hoare and A.A. Tseytlin, On string theory on AdS3 × S3 × T4 with mixed 3-form flux: tree-level S-matrix, Nucl. Phys. B 873 (2013) 682 [arXiv:1303.1037] [INSPIRE].
B. Hoare, A. Stepanchuk and A.A. Tseytlin, Giant magnon solution and dispersion relation in string theory in AdS3 × S3 × T4 with mixed flux, Nucl. Phys. B 879 (2014) 318 [arXiv:1311.1794] [INSPIRE].
R.A. Janik, The AdS5 × S5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D 73 (2006) 086006 [hep-th/0603038] [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and Crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefański, A. Torrielli and O. Ohlsson Sax, On the dressing factors, Bethe equations and Yangian symmetry of strings on AdS3 × S3 × T4, J. Phys. A 50 (2017) 024004 [arXiv:1607.00914] [INSPIRE].
D. Gepner and E. Witten, String Theory on Group Manifolds, Nucl. Phys. B 278 (1986) 493 [INSPIRE].
S. Chaudhuri and J.A. Schwartz, A Criterion for Integrably Marginal Operators, Phys. Lett. B 219 (1989) 291 [INSPIRE].
S. Förste and D. Roggenkamp, Current current deformations of conformal field theories, and WZW models, JHEP 05 (2003) 071 [hep-th/0304234] [INSPIRE].
A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \)-deformed 2D Quantum Field Theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
T. Dray and G. ’t Hooft, The Gravitational Shock Wave of a Massless Particle, Nucl. Phys. B 253 (1985) 173 [INSPIRE].
G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A.A. Tseytlin, Scale invariance of the η-deformed AdS5 × S5 superstring, T-duality and modified type-II equations, Nucl. Phys. B 903 (2016) 262 [arXiv:1511.05795] [INSPIRE].
L. Wulff and A.A. Tseytlin, κ-symmetry of superstring σ-model and generalized 10d supergravity equations, JHEP 06 (2016) 174 [arXiv:1605.04884] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2008.07603
Rights and permissions
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.
About this article
Cite this article
Bocconcello, M., Masuda, I., Seibold, F.K. et al. S matrix for a three-parameter integrable deformation of AdS3 × S3 strings. J. High Energ. Phys. 2020, 22 (2020). https://doi.org/10.1007/JHEP11(2020)022
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2020)022