Abstract
The worldsheet S matrix of strings on the AdS3 × S3 × T 4 background is almost entirely fixed by symmetries, up to five functions — the dressing factors. These must satisfy several consistency conditions, in particular a set of crossing equations. We find that the existing proposal for the dressing factors, while crossing invariant, violates some of these consistency conditions. We put forward a new set of dressing factors and discuss in detail their analytic properties in the string and mirror region, as well as under bound-state fusion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
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].
A. Sfondrini, Towards integrability for AdS3/CFT2, J. Phys. A 48 (2015) 023001 [arXiv:1406.2971] [INSPIRE].
R. Borsato, O. Ohlsson Sax and A. Sfondrini, A dynamic \( \mathfrak{su}{\left(\left.1\right|1\right)}^2 \) S-matrix for AdS3/CFT2, JHEP 04 (2013) 113 [arXiv:1211.5119] [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].
R. Borsato, O. Ohlsson Sax, A. Sfondrini, B. Stefański and A. Torrielli, The all-loop integrable spin-chain for strings on AdS3 × S3 × T 4: the massive sector, JHEP 08 (2013) 043 [arXiv:1303.5995] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański, Towards the all-loop worldsheet S matrix for AdS3 × S3 × T 4, Phys. Rev. Lett. 113 (2014) 131601 [arXiv:1403.4543] [INSPIRE].
R. Borsato, O. Ohlsson Sax, A. Sfondrini and B. Stefański, The complete AdS3 × S3 × T 4 worldsheet S matrix, JHEP 10 (2014) 066 [arXiv:1406.0453] [INSPIRE].
S. Frolov and A. Sfondrini, Massless S matrices for AdS3/CFT2, arXiv:2112.08895 [INSPIRE].
R. A. Janik, The AdS5 × S5 superstring worldsheet S-matrix and crossing symmetry, Phys. Rev. D 73 (2006) 086006 [hep-th/0603038] [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].
L. Castillejo, R. H. Dalitz and F. J. Dyson, Low’s scattering equation for the charged and neutral scalar theories, Phys. Rev. 101 (1956) 453 [INSPIRE].
N. Beisert, B. Eden and M. Staudacher, Transcendentality and crossing, J. Stat. Mech. 0701 (2007) P01021 [hep-th/0610251] [INSPIRE].
N. Dorey, D. M. Hofman and J. M. Maldacena, On the singularities of the magnon S-matrix, Phys. Rev. D 76 (2007) 025011 [hep-th/0703104] [INSPIRE].
G. Arutyunov and S. Frolov, The dressing factor and crossing equations, J. Phys. A 42 (2009) 425401 [arXiv:0904.4575] [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].
G. Arutyunov and S. Frolov, On string S-matrix, bound states and TBA, JHEP 12 (2007) 024 [arXiv:0710.1568] [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].
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].
G. Giribet, C. Hull, M. Kleban, M. Porrati and E. Rabinovici, Superstrings on AdS3 at k = 1, JHEP 08 (2018) 204 [arXiv:1803.04420] [INSPIRE].
L. Eberhardt, M. R. Gaberdiel and R. Gopakumar, The worldsheet dual of the symmetric product CFT, JHEP 04 (2019) 103 [arXiv:1812.01007] [INSPIRE].
L. Eberhardt, A perturbative CFT dual for pure NS-NS AdS3 strings, J. Phys. A 55 (2022) 064001 [arXiv:2110.07535] [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].
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 × T 4, J. Phys. A 50 (2017) 024004 [arXiv:1607.00914] [INSPIRE].
G. Arutyunov, S. Frolov and M. Staudacher, Bethe ansatz for quantum strings, JHEP 10 (2004) 016 [hep-th/0406256] [INSPIRE].
N. Beisert, R. Hernández and E. López, A crossing-symmetric phase for AdS5 × S5 strings, JHEP 11 (2006) 070 [hep-th/0609044] [INSPIRE].
A. Fontanella and A. Torrielli, Geometry of massless scattering in integrable superstring, JHEP 06 (2019) 116 [arXiv:1903.10759] [INSPIRE].
B. Hoare, A. Stepanchuk and A. A. Tseytlin, Giant magnon solution and dispersion relation in string theory in AdS3 × S3 × T 4 with mixed flux, Nucl. Phys. B 879 (2014) 318 [arXiv:1311.1794] [INSPIRE].
T. Lloyd, O. Ohlsson Sax, A. Sfondrini and B. Stefański, Jr., The complete worldsheet S matrix of superstrings on AdS3 × S3 × T 4 with mixed three-form flux, Nucl. Phys. B 891 (2015) 570 [arXiv:1410.0866] [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].
B. Eden, D. l. Plat and A. Sfondrini, Integrable bootstrap for AdS3/CFT2 correlation functions, JHEP 08 (2021) 049 [arXiv:2102.08365] [INSPIRE].
O. Ohlsson Sax and B. Stefański, On the singularities of the R-R AdS3 × S3 × T 4 S matrix, J. Phys. A 53 (2020) 155402 [arXiv:1912.04320] [INSPIRE].
S. Frolov and A. Sfondrini, Mirror thermodynamic Bethe ansatz for AdS3/CFT2, JHEP 03 (2022) 138 [arXiv:2112.08898] [INSPIRE].
P. Dorey and R. Tateo, Excited states by analytic continuation of TBA equations, Nucl. Phys. B 482 (1996) 639 [hep-th/9607167] [INSPIRE].
A. Fontanella, O. Ohlsson Sax, B. Stefański and A. Torrielli, The effectiveness of relativistic invariance in AdS3, JHEP 07 (2019) 105 [arXiv:1905.00757] [INSPIRE].
R. Hernández and E. López, Quantum corrections to the string Bethe ansatz, JHEP 07 (2006) 004 [hep-th/0603204] [INSPIRE].
G. Arutyunov and S. Frolov, On AdS5 × S5 string S-matrix, Phys. Lett. B 639 (2006) 378 [hep-th/0604043] [INSPIRE].
A. B. Zamolodchikov, From tricritical Ising to critical Ising by thermodynamic Bethe ansatz, Nucl. Phys. B 358 (1991) 524 [INSPIRE].
H.-Y. Chen, N. Dorey and K. Okamura, On the scattering of magnon boundstates, JHEP 11 (2006) 035 [hep-th/0608047] [INSPIRE].
N. Rughoonauth, P. Sundin and L. Wulff, Near BMN dynamics of the AdS3 × S3 × S3 × S1 superstring, JHEP 07 (2012) 159 [arXiv:1204.4742] [INSPIRE].
P. Sundin and L. Wulff, Worldsheet scattering in AdS3/CFT2, JHEP 07 (2013) 007 [arXiv:1302.5349] [INSPIRE].
O. T. Engelund, R. W. McKeown and R. Roiban, Generalized unitarity and the worldsheet S matrix in AdSn × Sn × M 10−2n, JHEP 08 (2013) 023 [arXiv:1304.4281] [INSPIRE].
R. Roiban, P. Sundin, A. Tseytlin and L. Wulff, The one-loop worldsheet S-matrix for the AdSn × Sn × T 10−2n superstring, JHEP 08 (2014) 160 [arXiv:1407.7883] [INSPIRE].
L. Bianchi and B. Hoare, AdS3 × S3 × M 4 string S-matrices from unitarity cuts, JHEP 08 (2014) 097 [arXiv:1405.7947] [INSPIRE].
P. Sundin and L. Wulff, The complete one-loop BMN S-matrix in AdS3 × S3 × T 4, JHEP 06 (2016) 062 [arXiv:1605.01632] [INSPIRE].
J. M. Maldacena and I. Swanson, Connecting giant magnons to the pp-wave: an interpolating limit of AdS5 × S5, Phys. Rev. D 76 (2007) 026002 [hep-th/0612079] [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].
P. Sundin and L. Wulff, The AdSn × Sn × T 10−2n BMN string at two loops, JHEP 11 (2015) 154 [arXiv:1508.04313] [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].
B. Hoare and A. A. Tseytlin, On string theory on AdS3 × S3 × T 4 with mixed 3-form flux: tree-level S-matrix, Nucl. Phys. B 873 (2013) 682 [arXiv:1303.1037] [INSPIRE].
S. Frolov and A. Sfondrini, Dressing factors for mixed-flux AdS3/CFT2, in preparation.
R. Borsato, O. Ohlsson Sax and A. Sfondrini, All-loop Bethe ansatz equations for AdS3/CFT2, JHEP 04 (2013) 116 [arXiv:1212.0505] [INSPIRE].
F. Seibold and A. Sfondrini, Transfer matrices of AdS3/CFT2, in preparation.
H. J. de Vega and J. M. Maillet, Renormalization character and quantum S matrix for a classically integrable theory, Phys. Lett. B 101 (1981) 302 [INSPIRE].
G. Bonneau and F. Delduc, S matrix properties versus renormalizability in two-dimensional O(N) symmetric models, Nucl. Phys. B 250 (1985) 561 [INSPIRE].
B. Hoare and A. A. Tseytlin, Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS5 × S5 superstring theory, Nucl. Phys. B 851 (2011) 161 [arXiv:1104.2423] [INSPIRE].
M. Goykhman and E. Ivanov, Worldsheet supersymmetry of Pohlmeyer-reduced AdSn × Sn superstrings, JHEP 09 (2011) 078 [arXiv:1104.0706] [INSPIRE].
T. J. Hollowood and J. L. Miramontes, The AdS5 × S5 semi-symmetric space sine-Gordon theory, JHEP 05 (2011) 136 [arXiv:1104.2429] [INSPIRE].
A. Babichenko, A. Dekel and O. Ohlsson Sax, Finite-gap equations for strings on AdS3 × S3 × T 4 with mixed 3-form flux, JHEP 11 (2014) 122 [arXiv:1405.6087] [INSPIRE].
P. Sundin and L. Wulff, One- and two-loop checks for the AdS3 × S3 × T 4 superstring with mixed flux, J. Phys. A 48 (2015) 105402 [arXiv:1411.4662] [INSPIRE].
A. Stepanchuk, String theory in AdS3 × S3 × T 4 with mixed flux: semiclassical and 1-loop phase in the S-matrix, J. Phys. A 48 (2015) 195401 [arXiv:1412.4764] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory, arXiv:1505.06745 [INSPIRE].
B. Eden and A. Sfondrini, Tessellating cushions: four-point functions in N = 4 SYM, JHEP 10 (2017) 098 [arXiv:1611.05436] [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of correlation functions, JHEP 01 (2017) 130 [arXiv:1611.05577] [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].
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: 2112.08896
Correspondent fellow at Steklov Mathematical Institute, Moscow, Russia. (Sergey Frolov)
IBM Einstein Fellow. (Alessandro Sfondrini)
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
Frolov, S., Sfondrini, A. New dressing factors for AdS3/CFT2. J. High Energ. Phys. 2022, 162 (2022). https://doi.org/10.1007/JHEP04(2022)162
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2022)162