Papers
Topics
Authors
Recent
Search
2000 character limit reached

All Jordanian deformations of the $AdS_5 \times S^5$ superstring

Published 21 Dec 2022 in hep-th | (2212.11269v2)

Abstract: We explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on $\mathfrak{psu}(2,2|4)$, corresponding to Jordanian Yang-Baxter deformations of the $AdS_5\times S5$ superstring. Such deformations preserve the classical integrability of the underlying sigma-model and thus are a subclass of all possible integrable deformations. The deformations that we consider are divided into two families, unimodular and non-unimodular ones. The former ensure that the deformed backgrounds are still solutions of the type IIB supergravity equations. For the simplest unimodular solutions, we find that the corresponding backgrounds preserve a number $N<32$ of supercharges that can be $N=12,8,6,4,0$.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (50)
  1. O. Lunin and J. M. Maldacena, “Deforming field theories with U⁢(1)×U⁢(1)𝑈1𝑈1U(1)\times U(1)italic_U ( 1 ) × italic_U ( 1 ) global symmetry and their gravity duals”, JHEP 0505, 033 (2005), hep-th/0502086.
  2. S. Frolov, “Lax pair for strings in Lunin-Maldacena background”, JHEP 0505, 069 (2005), hep-th/0503201.
  3. S. A. Frolov, R. Roiban and A. A. Tseytlin, “Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory”, JHEP 0507, 045 (2005), hep-th/0503192.
  4. C. Klimcik, “Yang-Baxter sigma models and dS/AdS T duality”, JHEP 0212, 051 (2002), hep-th/0210095.
  5. C. Klimcik, “On integrability of the Yang-Baxter sigma-model”, J.Math.Phys. 50, 043508 (2009), arxiv:0802.3518.
  6. F. Delduc, M. Magro and B. Vicedo, “On classical q𝑞qitalic_q-deformations of integrable sigma-models”, JHEP 1311, 192 (2013), arxiv:1308.3581.
  7. F. Delduc, M. Magro and B. Vicedo, “An integrable deformation of the AdS×5{}_{5}\timesstart_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT ×S55{}^{5}start_FLOATSUPERSCRIPT 5 end_FLOATSUPERSCRIPT superstring action”, Phys.Rev.Lett. 112, 051601 (2014), arxiv:1309.5850.
  8. I. Kawaguchi, T. Matsumoto and K. Yoshida, “Jordanian deformations of the A⁢d⁢S5⁢x⁢S5𝐴𝑑subscript𝑆5𝑥superscript𝑆5AdS_{5}xS^{5}italic_A italic_d italic_S start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT italic_x italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstring”, JHEP 1404, 153 (2014), arxiv:1401.4855.
  9. S. J. van Tongeren, “On classical Yang-Baxter based deformations of the AdS55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT × S55{}^{5}start_FLOATSUPERSCRIPT 5 end_FLOATSUPERSCRIPT superstring”, JHEP 1506, 048 (2015), arxiv:1504.05516.
  10. K. Sfetsos, “Integrable interpolations: From exact CFTs to non-Abelian T-duals”, Nucl.Phys. B880, 225 (2014), arxiv:1312.4560.
  11. T. J. Hollowood, J. L. Miramontes and D. M. Schmidtt, “Integrable Deformations of Strings on Symmetric Spaces”, JHEP 1411, 009 (2014), arxiv:1407.2840.
  12. T. J. Hollowood, J. L. Miramontes and D. M. Schmidtt, “An Integrable Deformation of the AdS×5{}_{5}\timesstart_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT ×S55{}^{5}start_FLOATSUPERSCRIPT 5 end_FLOATSUPERSCRIPT Superstring”, J.Phys. A47, 495402 (2014), arxiv:1409.1538.
  13. D. C. Thompson, “An Introduction to Generalised Dualities and their Applications to Holography and Integrability”, PoS CORFU2018, 099 (2019), arxiv:1904.11561.
  14. B. Hoare, “Integrable deformations of sigma models”, J. Phys. A 55, 093001 (2022), arxiv:2109.14284.
  15. R. Borsato and L. Wulff, “Target space supergeometry of η𝜂\etaitalic_η and λ𝜆\lambdaitalic_λ-deformed strings”, JHEP 1610, 045 (2016), arxiv:1608.03570.
  16. B. Hoare and F. K. Seibold, “Supergravity backgrounds of the η𝜂\etaitalic_η-deformed AdS×2S2×T6{}_{2}\times S^{2}\times T^{6}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT × italic_T start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT and AdS×5S5{}_{5}\times S^{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstrings”, JHEP 1901, 125 (2019), arxiv:1811.07841.
  17. K. Sfetsos and D. C. Thompson, “Spacetimes for λ𝜆\lambdaitalic_λ-deformations”, JHEP 1412, 164 (2014), arxiv:1410.1886.
  18. C. Appadu and T. J. Hollowood, “Beta function of k deformed AdS55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT × S55{}^{5}start_FLOATSUPERSCRIPT 5 end_FLOATSUPERSCRIPT string theory”, JHEP 1511, 095 (2015), arxiv:1507.05420.
  19. R. Borsato and S. Driezen, “Supergravity solution-generating techniques and canonical transformations of σ𝜎\sigmaitalic_σ-models from O⁢(D,D)𝑂𝐷𝐷O(D,D)italic_O ( italic_D , italic_D )”, JHEP 2105, 180 (2021), arxiv:2102.04498.
  20. R. Borsato, S. Driezen and F. Hassler, “An algebraic classification of solution generating techniques”, Phys. Lett. B 823, 136771 (2021), arxiv:2109.06185.
  21. N. Beisert et al., “Review of AdS/CFT Integrability: An Overview”, Lett. Math. Phys. 99, 3 (2012), arxiv:1012.3982.
  22. R. Borsato and L. Wulff, “On non-abelian T-duality and deformations of supercoset string sigma-models”, JHEP 1710, 024 (2017), arxiv:1706.10169.
  23. R. Borsato and L. Wulff, “Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings”, JHEP 1808, 027 (2018), arxiv:1806.04083.
  24. G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A. A. Tseytlin, “Scale invariance of the η𝜂\etaitalic_η-deformed A⁢d⁢S5×S5𝐴𝑑subscript𝑆5superscript𝑆5AdS_{5}\times S^{5}italic_A italic_d italic_S start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT superstring, T-duality and modified type II equations”, Nucl. Phys. B903, 262 (2016), arxiv:1511.05795.
  25. L. Wulff and A. A. Tseytlin, “Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations”, JHEP 1606, 174 (2016), arxiv:1605.04884.
  26. S. J. van Tongeren, “Unimodular jordanian deformations of integrable superstrings”, SciPost Phys. 7, 011 (2019), arxiv:1904.08892.
  27. D. Osten and S. J. van Tongeren, “Abelian Yang–Baxter deformations and TsT transformations”, Nucl. Phys. B915, 184 (2017), arxiv:1608.08504.
  28. L. F. Alday, G. Arutyunov and S. Frolov, “Green-Schwarz strings in TsT-transformed backgrounds”, JHEP 0606, 018 (2006), hep-th/0512253.
  29. N. Beisert and R. Roiban, “Beauty and the twist: The Bethe ansatz for twisted N=4 SYM”, JHEP 0508, 039 (2005), hep-th/0505187.
  30. M. de Leeuw and S. J. van Tongeren, “The spectral problem for strings on twisted A⁢d⁢S5×S5𝐴𝑑subscript𝑆5superscript𝑆5AdS_{5}\times S^{5}italic_A italic_d italic_S start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × italic_S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT”, Nucl. Phys. B860, 339 (2012), arxiv:1201.1451.
  31. V. Kazakov, “Quantum Spectral Curve of γ𝛾\gammaitalic_γ-twisted 𝒩=4𝒩4{\cal N}=4caligraphic_N = 4 SYM theory and fishnet CFT”, arxiv:1802.02160, in: “Ludwig Faddeev Memorial Volume”, ed.: M.-L. Ge, A. J. Niemi, K. K. Phua and L. A. Takhtajan, 293–342p.
  32. T. Meier and S. J. van Tongeren, “Quadratic twist-noncommutative gauge theory”, arxiv:2301.08757.
  33. R. Borsato, S. Driezen and J. L. Miramontes, “Homogeneous Yang-Baxter deformations as undeformed yet twisted models”, JHEP 2204, 053 (2022), arxiv:2112.12025.
  34. T. Matsumoto and K. Yoshida, “Yang–Baxter sigma models based on the CYBE”, Nucl. Phys. B893, 287 (2015), arxiv:1501.03665.
  35. B. Vicedo, “Deformed integrable σ𝜎\sigmaitalic_σ-models, classical R-matrices and classical exchange algebra on Drinfel’d doubles”, J. Phys. A 48, 355203 (2015), arxiv:1504.06303.
  36. S. J. Van Tongeren, “On Yang–Baxter models, twist operators, and boundary conditions”, J. Phys. A 51, 305401 (2018), arxiv:1804.05680.
  37. R. Borsato, S. Driezen, J. M. Nieto García and L. Wyss, “Semiclassical spectrum of a Jordanian deformation of AdS5×S5”, Phys. Rev. D 106, 066015 (2022), arxiv:2207.14748.
  38. R. Borsato and L. Wulff, “Marginal deformations of WZW models and the classical Yang-Baxter equation”, J. Phys. A52, 225401 (2019), arxiv:1812.07287.
  39. V. N. Tolstoy, “Chains of extended Jordanian twists for Lie superalgebras”, ArXiv Mathematics e-prints ,  (2004), math/0402433.
  40. J. Patera, P. Winternitz and H. Zassenhaus, “The Maximal Solvable Subgroups Of The S⁢u⁢(p,q)𝑆𝑢𝑝𝑞Su(p,q)italic_S italic_u ( italic_p , italic_q ) Groups And All Subgroups Of S⁢u⁢(2,1)𝑆𝑢21Su(2,1)italic_S italic_u ( 2 , 1 )”, J. Math. Phys. 15, 1378 (1974).
  41. J. Patera, P. Winternitz and H. Zassenhaus, “The maximal solvable subgroups of SO(p,q) groups”, Journal of Mathematical Physics 15, 1932 (1974), http://scitation.aip.org/content/aip/journal/jmp/15/11/10.1063/1.1666559.
  42. B. Hoare and A. A. Tseytlin, “Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS55{}_{5}start_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT sigma-model”, J. Phys. A49, 494001 (2016), arxiv:1609.02550.
  43. R. Borsato and L. Wulff, “Integrable Deformations of T𝑇Titalic_T-Dual σ𝜎\sigmaitalic_σ Models”, Phys. Rev. Lett. 117, 251602 (2016), arxiv:1609.09834.
  44. S. J. van Tongeren, “Yang–Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory”, Nucl. Phys. B904, 148 (2016), arxiv:1506.01023.
  45. S. J. van Tongeren, “Almost abelian twists and AdS/CFT”, Phys. Lett. B765, 344 (2017), arxiv:1610.05677.
  46. T. Araujo, I. Bakhmatov, E. O. Colgáin, J. Sakamoto, M. M. Sheikh-Jabbari and K. Yoshida, “Yang-Baxter σ𝜎\sigmaitalic_σ-models, conformal twists, and noncommutative Yang-Mills theory”, Phys. Rev. D95, 105006 (2017), arxiv:1702.02861.
  47. T. Araujo, I. Bakhmatov, E. O. Colgáin, J.-i. Sakamoto, M. M. Sheikh-Jabbari and K. Yoshida, “Conformal twists, Yang–Baxter σ𝜎\sigmaitalic_σ-models & holographic noncommutativity”, J. Phys. A 51, 235401 (2018), arxiv:1705.02063.
  48. N. Beisert, “The su(2|2)conditional22(2|2)( 2 | 2 ) dynamic S-matrix”, Adv.Theor.Math.Phys. 12, 945 (2008), hep-th/0511082.
  49. J. A. Minahan, “Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills”, Lett. Math. Phys. 99, 33 (2012), arxiv:1012.3983.
  50. G. Arutyunov and S. Frolov, “Foundations of the AdS×5{}_{5}\timesstart_FLOATSUBSCRIPT 5 end_FLOATSUBSCRIPT ×S55{}^{5}start_FLOATSUPERSCRIPT 5 end_FLOATSUPERSCRIPT Superstring. Part I”, J.Phys. A42, 254003 (2009), arxiv:0901.4937.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up