Abstract
We examine integrable λ-deformations of SO(n + 1)/SO(n) coset CFTs and their analytic continuations. We provide an interpretation of the deformation as a squashing of the corresponding coset σ-model’s target space. We realise the λ-deformation for n = 5 case as a solution to supergravity supported by non-vanishing five-form and dilaton. This interpolates between the coset CFT SO(4, 2)/SO(4, 1) × SO(6)/SO(5) constructed as a gauged WZW model and the non-Abelian T-dual of the AdS5 × S5 spacetime.
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].
J.A. Minahan and K. Zarembo, The Bethe ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].
W. Heisenberg, Zur Theorie des Ferromagnetismus (in German), Z. Phys. 49 (1928) 619 [INSPIRE].
H. Bethe, Zur Theorie der Metalle (in German), Z. Phys. 71 (1931) 205 [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS5 × S5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].
L.D. Faddeev and G.P. Korchemsky, High-energy QCD as a completely integrable model, Phys. Lett. B 342 (1995) 311 [hep-th/9404173] [INSPIRE].
L.N. Lipatov, Asymptotic behavior of multicolor QCD at high energies in connection with exactly solvable spin models, JETP Lett. 59 (1994) 596 [Pisma Zh. Eksp. Teor. Fiz. 59 (1994) 571] [hep-th/9311037] [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].
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].
D. Giataganas, L.A. Pando Zayas and K. Zoubos, On marginal deformations and non-integrability, JHEP 01 (2014) 129 [arXiv:1311.3241] [INSPIRE].
S. Frolov, Lax pair for strings in Lunin-Maldacena background, JHEP 05 (2005) 069 [hep-th/0503201] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
P. Basu and L.A. Pando Zayas, Chaos rules out integrability of strings in AdS5 × T1,1, Phys. Lett. B 700 (2011) 243 [arXiv:1103.4107] [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].
C. Klimčík, Yang-Baxter σ-models and dS/AdS T duality, JHEP 12 (2002) 051 [hep-th/0210095] [INSPIRE].
K. Sfetsos, Integrable interpolations: from exact CFTs to non-Abelian T-duals, Nucl. Phys. B 880 (2014) 225 [arXiv:1312.4560] [INSPIRE].
E. Witten, Non-Abelian bosonization in two-dimensions, Commun. Math. Phys. 92 (1984) 455 [INSPIRE].
G. Itsios, K. Sfetsos, K. Siampos and A. Torrielli, The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories, Nucl. Phys. B 889 (2014) 64 [arXiv:1409.0554] [INSPIRE].
K. Bardakci, E. Rabinovici and B. Saering, String models with c < 1 components, Nucl. Phys. B 299 (1988) 151 [INSPIRE].
K. Gawedzki and A. Kupiainen, G/h conformal field theory from gauged WZW model, Phys. Lett. B 215 (1988) 119 [INSPIRE].
D. Karabali, Q.-H. Park, H.J. Schnitzer and Z. Yang, A GKO construction based on a path integral formulation of gauged Wess-Zumino-Witten actions, Phys. Lett. B 216 (1989) 307 [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].
J. Balog, P. Forgacs, Z. Horvath and L. Palla, A new family of SU(2) symmetric integrable σ-models, Phys. Lett. B 324 (1994) 403 [hep-th/9307030] [INSPIRE].
S.G. Rajeev, Non-Abelian bosonization without Wess-Zumino terms. 1. New current algebra, Phys. Lett. B 217 (1989) 123 [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].
B. Hoare, T.J. Hollowood and J.L. Miramontes, A relativistic relative of the magnon S-matrix, JHEP 11 (2011) 048 [arXiv:1107.0628] [INSPIRE].
B. Hoare, T.J. Hollowood and J.L. Miramontes, q-deformation of the AdS5 × S5 superstring S-matrix and its relativistic limit, JHEP 03 (2012) 015 [arXiv:1112.4485] [INSPIRE].
B. Hoare, T.J. Hollowood and J.L. Miramontes, Bound states of the q-deformed AdS5 × S5 superstring S-matrix, JHEP 10 (2012) 076 [arXiv:1206.0010] [INSPIRE].
B. Hoare, T.J. Hollowood and J.L. Miramontes, Restoring unitarity in the q-deformed world-sheet S-matrix, JHEP 10 (2013) 050 [arXiv:1303.1447] [INSPIRE].
G. Arutyunov, R. Borsato and S. Frolov, S-matrix for strings on η-deformed AdS5 × S5, JHEP 04 (2014) 002 [arXiv:1312.3542] [INSPIRE].
T.J. Hollowood, J.L. Miramontes and D.M. Schmidtt, An integrable deformation of the AdS5 × S5 superstring, J. Phys. A 47 (2014) 495402 [arXiv:1409.1538] [INSPIRE].
G. Itsios, K. Sfetsos and K. Siampos, The all-loop non-Abelian Thirring model and its RG flow, Phys. Lett. B 733 (2014) 265 [arXiv:1404.3748] [INSPIRE].
K. Sfetsos and K. Siampos, Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model, Nucl. Phys. B 885 (2014) 583 [arXiv:1405.7803] [INSPIRE].
R. Squellari, Yang-Baxter σ model: quantum aspects, Nucl. Phys. B 881 (2014) 502 [arXiv:1401.3197] [INSPIRE].
O. Lunin, R. Roiban and A.A. Tseytlin, Supergravity backgrounds for deformations of AdS n × Sn supercoset string models, Nucl. Phys. B 891 (2015) 106 [arXiv:1411.1066] [INSPIRE].
K. Sfetsos and D.C. Thompson, Spacetimes for λ-deformations, JHEP 12 (2014) 164 [arXiv:1410.1886] [INSPIRE].
D. Orlando, S. Reffert and L.I. Uruchurtu, Classical integrability of the squashed three-sphere, warped AdS3 and Schrödinger spacetime via T-duality, J. Phys. A 44 (2011) 115401 [arXiv:1011.1771] [INSPIRE].
I. Kawaguchi, D. Orlando and K. Yoshida, Yangian symmetry in deformed WZNW models on squashed spheres, Phys. Lett. B 701 (2011) 475 [arXiv:1104.0738] [INSPIRE].
I. Kawaguchi and K. Yoshida, Hybrid classical integrability in squashed σ-models, Phys. Lett. B 705 (2011) 251 [arXiv:1107.3662] [INSPIRE].
D. Orlando and L.I. Uruchurtu, Integrable superstrings on the squashed three-sphere, JHEP 10 (2012) 007 [arXiv:1208.3680] [INSPIRE].
K. Sfetsos, Gauged WZW models and non-Abelian duality, Phys. Rev. D 50 (1994) 2784 [hep-th/9402031] [INSPIRE].
E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].
K. Bardakci, M.J. Crescimanno and E. Rabinovici, Parafermions from coset models, Nucl. Phys. B 344 (1990) 344 [INSPIRE].
M. Roček, K. Schoutens and A. Sevrin, Off-shell WZW models in extended superspace, Phys. Lett. B 265 (1991) 303 [INSPIRE].
I. Bars and K. Sfetsos, Generalized duality and singular strings in higher dimensions, Mod. Phys. Lett. A 7 (1992) 1091 [hep-th/9110054] [INSPIRE].
E.S. Fradkin and V.Y. Linetsky, On space-time interpretation of the coset models in D < 26 critical string theory, Phys. Lett. B 277 (1992) 73 [INSPIRE].
I. Bars and K. Sfetsos, A superstring theory in four curved space-time dimensions, Phys. Lett. B 277 (1992) 269 [hep-th/9111040] [INSPIRE].
K. Pohlmeyer, Integrable Hamiltonian systems and interactions through quadratic constraints, Commun. Math. Phys. 46 (1976) 207 [INSPIRE].
M. Grigoriev and A.A. Tseytlin, Pohlmeyer reduction of AdS5 × S5 superstring σ-model, Nucl. Phys. B 800 (2008) 450 [arXiv:0711.0155] [INSPIRE].
I. Bakas, Q.-H. Park and H.-J. Shin, Lagrangian formulation of symmetric space sine-Gordon models, Phys. Lett. B 372 (1996) 45 [hep-th/9512030] [INSPIRE].
C.R. Fernandez-Pousa, M.V. Gallas, T.J. Hollowood and J.L. Miramontes, The symmetric space and homogeneous sine-Gordon theories, Nucl. Phys. B 484 (1997) 609 [hep-th/9606032] [INSPIRE].
Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-Abelian T-duality, Ramond fields and coset geometries, JHEP 06 (2011) 106 [arXiv:1104.5196] [INSPIRE].
K. Sfetsos and D.C. Thompson, On non-Abelian T-dual geometries with Ramond fluxes, Nucl. Phys. B 846 (2011) 21 [arXiv:1012.1320] [INSPIRE].
S.F. Hassan, T-duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [INSPIRE].
Ö. Kelekci, Y. Lozano, N.T. Macpherson and E. Ó. Colgáin, Supersymmetry and non-Abelian T-duality in type-II supergravity, Class. Quant. Grav. 32 (2015) 035014 [arXiv:1409.7406] [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].
P.M. Petropoulos and K. Sfetsos, Non-Abelian coset string backgrounds from asymptotic and initial data, JHEP 04 (2007) 033 [hep-th/0610055] [INSPIRE].
B. Vicedo, Deformed integrable σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles, arXiv:1504.06303 [INSPIRE].
B. Hoare and A.A. Tseytlin, On integrable deformations of superstring σ-models related to AdS n × Sn supercosets, Nucl. Phys. B 897 (2015) 448 [arXiv:1504.07213] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1504.02781
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Demulder, S., Sfetsos, K. & Thompson, D.C. Integrable λ-deformations: squashing coset CFTs and AdS5 × S5. J. High Energ. Phys. 2015, 19 (2015). https://doi.org/10.1007/JHEP07(2015)019
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2015)019