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Journal of High Energy Physics

, 2019:56 | Cite as

Yang-Baxter deformations of the AdS5 × S5 pure spinor superstring

  • Héctor A. Benítez
  • Victor O. RivellesEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We present integrable Yang-Baxter deformations of the AdS5 × S5 pure spinor superstring theory which were obtained by using homological perturbation theory. Its equations of motion and BRST symmetry are discussed and its Lax connection is derived. We also show that its target space background is the same generalized supergravity background found for Yang-Baxter deformations of the Green-Schwarz superstring in AdS5 × S5.

Keywords

Superstrings and Heterotic Strings Integrable Field Theories Sigma Models Supergravity Models 

Notes

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.

References

  1. [1]
    N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    D. Bombardelli et al., An integrability primer for the gauge-gravity correspondence: An introduction, J. Phys. A 49 (2016) 320301 [arXiv:1606.02945] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  3. [3]
    I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS 5 × S 5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].ADSGoogle Scholar
  4. [4]
    B.C. Vallilo, Flat currents in the classical AdS 5 × S 5 pure spinor superstring, JHEP 03 (2004) 037 [hep-th/0307018] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  5. [5]
    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].zbMATHGoogle Scholar
  6. [6]
    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].ADSCrossRefGoogle Scholar
  7. [7]
    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].ADSCrossRefzbMATHGoogle Scholar
  8. [8]
    I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS 5 × S 5 superstring, JHEP 04 (2014) 153 [arXiv:1401.4855] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    T. Matsumoto and K. Yoshida, Integrable deformations of the AdS 5 × S 5 superstring and the classical Yang-Baxter equation — Towards the gravity/CYBE correspondence —, J. Phys. Conf. Ser. 563 (2014) 012020 [arXiv:1410.0575] [INSPIRE].CrossRefGoogle Scholar
  10. [10]
    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].ADSCrossRefGoogle Scholar
  11. [11]
    G. Arutyunov, R. Borsato and S. Frolov, Puzzles of η-deformed AdS 5 × S 5, JHEP 12 (2015) 049 [arXiv:1507.04239] [INSPIRE].ADSGoogle Scholar
  12. [12]
    B. Hoare and S.J. van Tongeren, On Jordanian deformations of AdS 5 and supergravity, J. Phys. A 49 (2016) 434006 [arXiv:1605.03554] [INSPIRE].zbMATHGoogle Scholar
  13. [13]
    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].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    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].
  15. [15]
    R. Borsato and L. Wulff, Target space supergeometry of η and λ-deformed strings, JHEP 10 (2016) 045 [arXiv:1608.03570] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    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].ADSCrossRefGoogle Scholar
  17. [17]
    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].ADSCrossRefzbMATHGoogle Scholar
  18. [18]
    S.J. van Tongeren, On classical Yang-Baxter based deformations of the AdS 5 × S 5 superstring, JHEP 06 (2015) 048 [arXiv:1504.05516] [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    S.J. van Tongeren, Yang-Baxter deformations, AdS/CFT and twist-noncommutative gauge theory, Nucl. Phys. B 904 (2016) 148 [arXiv:1506.01023] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    D. Osten and S.J. van Tongeren, Abelian Yang-Baxter deformations and TsT transformations, Nucl. Phys. B 915 (2017) 184 [arXiv:1608.08504] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    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].zbMATHGoogle Scholar
  22. [22]
    B. Hoare and D.C. Thompson, Marginal and non-commutative deformations via non-abelian T-duality, JHEP 02 (2017) 059 [arXiv:1611.08020] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    R. Borsato and L. Wulff, Integrable Deformations of T-Dual σ Models, Phys. Rev. Lett. 117 (2016) 251602 [arXiv:1609.09834] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    R. Borsato and L. Wulff, On non-abelian T-duality and deformations of supercoset string σ-models, JHEP 10 (2017) 024 [arXiv:1706.10169] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    R. Borsato and L. Wulff, Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings, JHEP 08 (2018) 027 [arXiv:1806.04083] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    S.J. van Tongeren, Almost abelian twists and AdS/CFT, Phys. Lett. B 765 (2017) 344 [arXiv:1610.05677] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  27. [27]
    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].
  28. [28]
    T. Araujo, I. Bakhmatov, E. Ó. Colgáin, J.-i. Sakamoto, M.M. Sheikh-Jabbari and K. Yoshida, Conformal twists, Yang-Baxter σ-models & holographic noncommutativity, J. Phys. A 51 (2018) 235401 [arXiv:1705.02063] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  29. [29]
    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].
  30. [30]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    T. Araujo, E. Ó. Colgáin and H. Yavartanoo, Embedding the modified CYBE in Supergravity, Eur. Phys. J. C 78 (2018) 854 [arXiv:1806.02602] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    J.-I. Sakamoto and Y. Sakatani, Local β-deformations and Yang-Baxter σ-model, JHEP 06 (2018) 147 [arXiv:1803.05903] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    A. Mikhailov, Symmetries of massless vertex operators in AdS 5 × S 5, J. Geom. Phys. 62 (2012) 479 [arXiv:0903.5022] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    N. Berkovits and T. Fleury, Harmonic Superspace from the AdS 5 × S 5 Pure Spinor Formalism, JHEP 03 (2013) 022 [arXiv:1212.3296] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  36. [36]
    I. Ramirez and B.C. Vallilo, Worldsheet dilatation operator for the AdS superstring, JHEP 05 (2016) 129 [arXiv:1509.00769] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    N. Berkovits, Quantum consistency of the superstring in AdS 5 × S 5 background, JHEP 03 (2005) 041 [hep-th/0411170] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    P.A. Grassi and J. Kluson, Pure spinor strings in TsT deformed background, JHEP 03 (2007) 033 [hep-th/0611151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    D.M. Schmidtt, Exploring The Lambda Model Of The Hybrid Superstring, JHEP 10 (2016) 151 [arXiv:1609.05330] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    O.A. Bedoya, L.I. Bevilaqua, A. Mikhailov and V.O. Rivelles, Notes on β-deformations of the pure spinor superstring in AdS 5 × S 5, Nucl. Phys. B 848 (2011) 155 [arXiv:1005.0049] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  41. [41]
    A. Mikhailov, Cornering the unphysical vertex, JHEP 11 (2012) 082 [arXiv:1203.0677] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    N. Berkovits and O. Chandía, Superstring vertex operators in an AdS5 × S5 background, Nucl. Phys. B 596 (2001) 185 [hep-th/0009168] [INSPIRE].
  43. [43]
    A. Mikhailov, Vertex operators of ghost number three in Type IIB supergravity, Nucl. Phys. B 907 (2016) 509 [arXiv:1401.3783] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    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].
  45. [45]
    N. Berkovits and P.S. Howe, Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring, Nucl. Phys. B 635 (2002) 75 [hep-th/0112160] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    S.J. Van Tongeren, On Yang-Baxter models, twist operators and boundary conditions, J. Phys. A 51 (2018) 305401 [arXiv:1804.05680] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  47. [47]
    L. Mazzucato, Superstrings in AdS, Phys. Rept. 521 (2012) 1 [arXiv:1104.2604] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    N. Berkovits and C. Vafa, Towards a Worldsheet Derivation of the Maldacena Conjecture, JHEP 03 (2008) 031 [arXiv:0711.1799] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  49. [49]
    A. Mikhailov, A minimalistic pure spinor σ-model in AdS, JHEP 07 (2018) 155 [arXiv:1706.08158] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  50. [50]
    N. Berkovits, Simplifying and Extending the AdS 5 × S 5 Pure Spinor Formalism, JHEP 09 (2009) 051 [arXiv:0812.5074] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrazil

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