Abstract
We investigate Poisson-Lie duals of the η-deformed AdS2 ×S2 ×T6 superstring. The η-deformed background satisfies a generalisation of the type II supergravity equations. We discuss three Poisson-Lie duals, with respect to (i) the full \( \mathfrak{p}\mathfrak{s}\mathfrak{u}\left(1,\left.1\right|2\right) \) superalgebra, (ii) the full bosonic subalgebra and (iii) the Cartan subalgebra, for which the corresponding backgrounds are expected to satisfy the standard type II supergravity equations. The metrics and B-fields for the first two cases are the same and given by an analytic continuation of the λ-deformed model on AdS2 × S2 × T6 with the torus undeformed. However, the RR fluxes and dilaton will differ. Focusing on the second case we explicitly derive the background and show agreement with an analytic continuation of a known embedding of the λ-deformed model on AdS2 × S2 in type II supergravity.
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B. Hoare and F.K. Seibold, Poisson-Lie duals of the η deformed symmetric space σ-model, JHEP 11 (2017) 014 [arXiv:1709.01448] [INSPIRE].
C. Klimčík and P. Ševera, Dual non-Abelian duality and the Drinfeld double, Phys. Lett. B 351 (1995) 455 [hep-th/9502122] [INSPIRE].
C. Klimčík, Poisson-Lie T-duality, Nucl. Phys. Proc. Suppl. 46 (1996) 116 [hep-th/9509095] [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, On classical q-deformations of integrable σ-models, JHEP 11 (2013) 192 [arXiv:1308.3581] [INSPIRE].
H. Eichenherr and M. Forger, On the dual symmetry of the non-linear σ-models, Nucl. Phys. B 155 (1979) 381 [INSPIRE].
H. Eichenherr and M. Forger, More about non-linear σ-models on symmetric spaces, Nucl. Phys. B 164 (1980) 528 [Erratum ibid. B 282 (1987) 745] [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].
J.-G. Zhou, Super 0-brane and GS superstring actions on AdS 2 × S 2, Nucl. Phys. B 559 (1999) 92 [hep-th/9906013] [INSPIRE].
N. Berkovits, M. Bershadsky, T. Hauer, S. Zhukov and B. Zwiebach, Superstring theory on AdS 2 × S 2 as a coset supermanifold, Nucl. Phys. B 567 (2000) 61 [hep-th/9907200] [INSPIRE].
K. Zarembo, Strings on semisymmetric superspaces, JHEP 05 (2010) 002 [arXiv:1003.0465] [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].
M.B. Green and J.H. Schwarz, Covariant description of superstrings, Phys. Lett. B 136 (1984) 367 [INSPIRE].
M.B. Green and J.H. Schwarz, Properties of the covariant formulation of superstring theories, Nucl. Phys. B 243 (1984) 285 [INSPIRE].
E. Witten, Twistor-like transform in ten-dimensions, Nucl. Phys. B 266 (1986) 245 [INSPIRE].
M.T. Grisaru, P.S. Howe, L. Mezincescu, B. Nilsson and P.K. Townsend, N = 2 superstrings in a supergravity background, Phys. Lett. 162B (1985) 116 [INSPIRE].
D. Sorokin, A. Tseytlin, L. Wulff and K. Zarembo, Superstrings in AdS 2 × S 2 × T 6, J. Phys. A 44 (2011) 275401 [arXiv:1104.1793] [INSPIRE].
B. Hoare and S.J. van Tongeren, Non-split and split deformations of AdS5, J. Phys. A 49 (2016) 484003 [arXiv:1605.03552] [INSPIRE].
T. Araujo, E. Ó Colgáin, J. Sakamoto, M.M. Sheikh-Jabbari and K. Yoshida, I in generalized supergravity, Eur. Phys. J. C 77 (2017) 739 [arXiv:1708.03163] [INSPIRE].
F. Delduc, S. Lacroix, M. Magro and B. Vicedo, On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models, J. Phys. A 49 (2016) 415402 [arXiv:1606.01712] [INSPIRE].
F. Delduc, T. Kameyama, M. Magro and B. Vicedo, Affine q-deformed symmetry and the classical Yang-Baxter σ-model, JHEP 03 (2017) 126 [arXiv:1701.03691] [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].
C. Klimčík and P. Ševera, Poisson-Lie T duality and loop groups of Drinfeld doubles, Phys. Lett. B 372 (1996) 65 [hep-th/9512040] [INSPIRE].
C. Klimčík and P. Ševera, NonAbelian momentum winding exchange, Phys. Lett. B 383 (1996) 281 [hep-th/9605212] [INSPIRE].
C. Klimčík and P. Ševera, Dressing cosets, Phys. Lett. B 381 (1996) 56 [hep-th/9602162] [INSPIRE].
R. Squellari, Dressing cosets revisited, Nucl. Phys. B 853 (2011) 379 [arXiv:1105.0162] [INSPIRE].
K. Sfetsos, Duality invariant class of two-dimensional field theories, Nucl. Phys. B 561 (1999) 316 [hep-th/9904188] [INSPIRE].
D. Lüst and D. Osten, Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality, JHEP 05 (2018) 165 [arXiv:1803.03971] [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].
C. Klimčík, η and λ deformations as ε-models, Nucl. Phys. B 900 (2015) 259 [arXiv:1508.05832] [INSPIRE].
S. Driezen, A. Sevrin and D.C. Thompson, D-branes in λ-deformations, arXiv:1806.10712 [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, 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, Integrable deformations of strings on symmetric spaces, JHEP 11 (2014) 009 [arXiv:1407.2840] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, On non-Abelian duality, Nucl. Phys. B 424 (1994) 155 [hep-th/9403155] [INSPIRE].
S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer and G. Veneziano, Remarks on non-Abelian duality, Nucl. Phys. B 435 (1995) 147 [hep-th/9409011] [INSPIRE].
E. Tyurin and R. von Unge, Poisson-Lie T-duality: the path integral derivation, Phys. Lett. B 382 (1996) 233 [hep-th/9512025] [INSPIRE].
A. Bossard and N. Mohammedi, Poisson-Lie duality in the string effective action, Nucl. Phys. B 619 (2001) 128 [hep-th/0106211] [INSPIRE].
R. Von Unge, Poisson-Lie T-plurality, JHEP 07 (2002) 014 [hep-th/0205245] [INSPIRE].
L. Hlavatý and L. Šnobl, Poisson-Lie T plurality of three-dimensional conformally invariant σ-models, JHEP 05 (2004) 010 [hep-th/0403164] [INSPIRE].
L. Hlavatý and L. Šnobl, Poisson-Lie T-plurality of three-dimensional conformally invariant σ-models. II. Nondiagonal metrics and dilaton puzzle, JHEP 10 (2004) 045 [hep-th/0408126] [INSPIRE].
B. Jurčo and J. Vysoký, Poisson-Lie T-duality of string effective actions: a new approach to the dilaton puzzle, J. Geom. Phys. 130 (2018) 1 [arXiv:1708.04079] [INSPIRE].
G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A.A. Tseytlin, Scale invariance of the η-deformed AdS 5 × S 5 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].
B. Hoare and A.A. Tseytlin, Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS 5 σ-model, J. Phys. A 49 (2016) 494001 [arXiv:1609.02550] [INSPIRE].
M. Hong, Y. Kim and E. Ó Colgáin, On non-Abelian T-duality for non-semisimple groups, arXiv:1801.09567 [INSPIRE].
L. Wulff, Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly, Phys. Lett. B 781 (2018) 417 [arXiv:1803.07391] [INSPIRE].
Y. Sakatani, S. Uehara and K. Yoshida, Generalized gravity from modified DFT, JHEP 04 (2017) 123 [arXiv:1611.05856] [INSPIRE].
A. Baguet, M. Magro and H. Samtleben, Generalized IIB supergravity from exceptional field theory, JHEP 03 (2017) 100 [arXiv:1612.07210] [INSPIRE].
J.-i. Sakamoto, Y. Sakatani and K. Yoshida, Weyl invariance for generalized supergravity backgrounds from the doubled formalism, PTEP 2017 (2017) 053B07 [arXiv:1703.09213] [INSPIRE].
J.J. Fernandez-Melgarejo, J.-i. Sakamoto, Y. Sakatani and K. Yoshida, T-folds from Yang-Baxter deformations, JHEP 12 (2017) 108 [arXiv:1710.06849] [INSPIRE].
J.-I. Sakamoto and Y. Sakatani, Local β-deformations and Yang-Baxter σ-model, JHEP 06 (2018) 147 [arXiv:1803.05903] [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].
V.A. Fateev, E. Onofri and A.B. Zamolodchikov, The sausage model (integrable deformations of O(3) σ-model), Nucl. Phys. B 406 (1993) 521 [INSPIRE].
R. Borsato and L. Wulff, Target space supergeometry of η and λ-deformed strings, JHEP 10 (2016) 045 [arXiv:1608.03570] [INSPIRE].
I. Bakhmatov, Ö. Kelekci, E. Ó Colgáin and M.M. Sheikh-Jabbari, Classical Yang-Baxter equation from supergravity, Phys. Rev. D 98 (2018) 021901 [arXiv:1710.06784] [INSPIRE].
T. Araujo, E. O Colgáin and H. Yavartanoo, Embedding the modified CYBE in Supergravity, arXiv:1806.02602 [INSPIRE].
R. Borsato, A.A. Tseytlin and L. Wulff, Supergravity background of λ-deformed model for AdS 2 × S 2 supercoset, Nucl. Phys. B 905 (2016) 264 [arXiv:1601.08192] [INSPIRE].
B. Hoare and A.A. Tseytlin, Type IIB supergravity solution for the T-dual of the η-deformed AdS 5 × S 5 superstring, JHEP 10 (2015) 060 [arXiv:1508.01150] [INSPIRE].
K. Sfetsos and D.C. Thompson, Spacetimes for λ-deformations, JHEP 12 (2014) 164 [arXiv:1410.1886] [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].
G. Arutyunov, R. Borsato and S. Frolov, Puzzles of η-deformed AdS 5 × S 5, JHEP 12 (2015) 049 [arXiv:1507.04239] [INSPIRE].
C.M. Hull, Timelike T-duality, de Sitter space, large N gauge theories and topological field theory, JHEP 07 (1998) 021 [hep-th/9806146] [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].
P. Ševera, On integrability of 2-dimensional σ-models of Poisson-Lie type, JHEP 11 (2017) 015 [arXiv:1709.02213] [INSPIRE].
L. Wulff, Superisometries and integrability of superstrings, JHEP 05 (2014) 115 [arXiv:1402.3122] [INSPIRE].
L. Wulff, On integrability of strings on symmetric spaces, JHEP 09 (2015) 115 [arXiv:1505.03525] [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].
B. Hoare, A. Pittelli and A. Torrielli, Integrable S-matrices, massive and massless modes and the AdS 2 × S 2 superstring, JHEP 11 (2014) 051 [arXiv:1407.0303] [INSPIRE].
G. Arutyunov, M. de Leeuw and S.J. van Tongeren, The quantum deformed mirror TBA I, JHEP 10 (2012) 090 [arXiv:1208.3478] [INSPIRE].
G. Arutyunov, M. de Leeuw and S.J. van Tongeren, The quantum deformed mirror TBA II, JHEP 02 (2013) 012 [arXiv:1210.8185] [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].
R. Klabbers and S.J. van Tongeren, Quantum spectral curve for the eta-deformed AdS 5 × S 5 superstring, Nucl. Phys. B 925 (2017) 252 [arXiv:1708.02894] [INSPIRE].
C. Appadu, T.J. Hollowood, J.L. Miramontes, D. Price and D.M. Schmidtt, Giant magnons of string theory in the λ background, JHEP 07 (2017) 098 [arXiv:1704.05437] [INSPIRE].
G. Arutyunov and S.J. van Tongeren, AdS 5 × S 5 mirror model as a string σ-model, Phys. Rev. Lett. 113 (2014) 261605 [arXiv:1406.2304] [INSPIRE].
A. Pachoł and S.J. van Tongeren, Quantum deformations of the flat space superstring, Phys. Rev. D 93 (2016) 026008 [arXiv:1510.02389] [INSPIRE].
A. Yu. Alekseev, C. Klimčík and A.A. Tseytlin, Quantum Poisson-Lie T-duality and WZNW model, Nucl. Phys. B 458 (1996) 430 [hep-th/9509123] [INSPIRE].
G. Valent, C. Klimčík and R. Squellari, One loop renormalizability of the Poisson-Lie σ-models, Phys. Lett. B 678 (2009) 143 [arXiv:0902.1459] [INSPIRE].
K. Sfetsos and K. Siampos, Quantum equivalence in Poisson-Lie T-duality, JHEP 06 (2009) 082 [arXiv:0904.4248] [INSPIRE].
S.D. Avramis, J.-P. Derendinger and N. Prezas, Conformal chiral boson models on twisted doubled tori and non-geometric string vacua, Nucl. Phys. B 827 (2010) 281 [arXiv:0910.0431] [INSPIRE].
K. Sfetsos, K. Siampos and D.C. Thompson, Renormalization of Lorentz non-invariant actions and manifest T-duality, Nucl. Phys. B 827 (2010) 545 [arXiv:0910.1345] [INSPIRE].
L. Hlavatý, J. Navrátil and L. Šnobl, On renormalization of Poisson-Lie T-plural σ-models, Acta Polytech. 53 (2013) 433 [arXiv:1212.5936] [INSPIRE].
F. Hassler, Poisson-Lie T-duality in double field theory, arXiv:1707.08624 [INSPIRE].
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Hoare, B., Seibold, F.K. Poisson-Lie duals of the η-deformed AdS2 × S2 × T6 superstring. J. High Energ. Phys. 2018, 107 (2018). https://doi.org/10.1007/JHEP08(2018)107
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DOI: https://doi.org/10.1007/JHEP08(2018)107