Advertisement

Non-Abelian T-duality as a transformation in Double Field Theory

  • Aybike Çatal-ÖzerEmail author
Open Access
Regular Article - Theoretical Physics
  • 38 Downloads

Abstract

Non-Abelian T-duality (NATD) is a solution generating transformation for supergravity backgrounds with non-Abelian isometries. We show that NATD can be de-scribed as a coordinate dependent O(d,d) transformation, where the dependence on the coordinates is determined by the structure constants of the Lie algebra associated with the isometry group. Besides making calculations significantly easier, this approach gives a natural embedding of NATD in Double Field Theory (DFT), a framework which provides an O(d,d) covariant formulation for effective string actions. As a result of this embedding, it becomes easy to prove that the NATD transformed backgrounds solve supergravity equations, when the isometry algebra is unimodular. If the isometry algebra is non-unimodular, the generalized dilaton field is forced to have a linear dependence on the dual coordinates, which implies that the resulting background solves generalized supergravity equations.

Keywords

String Duality Flux compactifications 

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]
    X.C. de la Ossa and F. Quevedo, Duality symmetries from nonAbelian isometries in string theory, Nucl. Phys.B 403 (1993) 377 [hep-th/9210021] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    E. Alvarez, L. Alvarez-Gaume and Y. Lozano, NonAbelian duality in WZW models, (1994) [INSPIRE].
  3. [3]
    A. Giveon and M. Roček, On nonAbelian duality, Nucl. Phys. B 421 (1994) 173 [hep-th/9308154] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    K. Sfetsos, Gauged WZW models and nonAbelian duality, Phys. Rev.D 50 (1994) 2784 [hep-th/9402031] [INSPIRE].ADSMathSciNetGoogle Scholar
  5. [5]
    E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, On nonAbelian duality, Nucl. Phys.B 424 (1994) 155 [hep-th/9403155] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    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].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-abelian T-duality, Ramond Fields and Coset Geometries, JHEP06 (2011) 106 [arXiv:1104.5196] [INSPIRE].
  8. [8]
    G. Itsios, Y. Lozano, E. O Colgain and K. Sfetsos, Non-Abelian T-duality and consistent truncations in type-II supergravity, JHEP08 (2012) 132 [arXiv:1205.2274] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    G. Itsios, C. Núñez, K. Sfetsos and D.C. Thompson, Non-Abelian T-duality and the AdS/CFT correspondence:new N = 1 backgrounds, Nucl. Phys.B 873 (2013) 1 [arXiv:1301.6755] [INSPIRE].
  10. [10]
    J. Jeong, O. Kelekci and E. O Colgain, An alternative IIB embedding of F (4) gauged supergravity, JHEP05 (2013) 079 [arXiv:1302.2105] [INSPIRE].
  11. [11]
    K. Sfetsos and D.C. Thompson, New \( \mathcal{N}=1 \)supersymmetric AdS 5backgrounds in Type IIA supergravity, JHEP11 (2014) 006 [arXiv:1408.6545] [INSPIRE].
  12. [12]
    E. Caceres, N.T. Macpherson and C. Núñez, New Type IIB Backgrounds and Aspects of Their Field Theory Duals, JHEP08 (2014) 107 [arXiv:1402.3294] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    N.T. Macpherson, C. Núñez, L.A. Pando Zayas, V.G.J. Rodgers and C.A. Whiting, Type IIB supergravity solutions with AdS 5from Abelian and non-Abelian T dualities, JHEP02 (2015) 040 [arXiv:1410.2650] [INSPIRE].Google Scholar
  14. [14]
    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].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    L.A. Pando Zayas, V.G.J. Rodgers and C.A. Whiting, Supergravity solutions with AdS 4from non-Abelian T-dualities, JHEP02 (2016) 061 [arXiv:1511.05991] [INSPIRE].Google Scholar
  16. [16]
    G. Itsios, Y. Lozano, J. Montero and C. Núñez, The AdS 5non-Abelian T-dual of Klebanov-Witten as a \( \mathcal{N}=1 \)linear quiver from M5-branes, JHEP09 (2017) 038 [arXiv:1705.09661] [INSPIRE].Google Scholar
  17. [17]
    R. Borsato and L. Wulff, Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings, JHEP08 (2018) 027 [arXiv:1806.04083] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    G. Arutyunov, S. Frolov, B. Hoare, R. Roiban and A.A. Tseytlin, Scale invariance of the η-deformed AdS 5× S 5superstring, T-duality and modified type-II equations, Nucl. Phys.B 903 (2016)262 [arXiv:1511.05795] [INSPIRE].
  19. [19]
    L. Wulff and A.A. Tseytlin, κ-symmetry of superstring σ-model and generalized 10d supergravity equations, JHEP06 (2016) 174 [arXiv:1605.04884] [INSPIRE].
  20. [20]
    M. Gasperini, R. Ricci and G. Veneziano, A Problem with nonAbelian duality?, Phys. Lett.B 319 (1993) 438 [hep-th/9308112] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer and G. Veneziano, Remarks on nonAbelian duality, Nucl. Phys.B 435 (1995) 147 [hep-th/9409011] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    M. Hong, Y. Kim and E. Ó. Colgáin, On non-Abelian T-duality for non-semisimple groups, Eur. Phys. J.C 78 (2018) 1025 [arXiv:1801.09567] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept.244 (1994) 77 [hep-th/9401139] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    M. Fukuma, T. Oota and H. Tanaka, Comments on T dualities of Ramond-Ramond potentials on tori, Prog. Theor. Phys.103 (2000) 425 [hep-th/9907132] [INSPIRE].
  25. [25]
    Y. Sakatani, Type II DFT solutions from Poisson-Lie T-duality/plurality, arXiv:1903.12175 [INSPIRE].
  26. [26]
    M. Bugden, Non-abelian T-folds, JHEP03 (2019) 189 [arXiv:1901.03782] [INSPIRE].
  27. [27]
    A. Catal-Ozer, Non-Abelian T-duality as an O(d, d) transformation, APCTP, Pohang, Korea, (2016) [https://www.apctp.org/plan.php/duality/1341].
  28. [28]
    A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys.B 350 (1991) 395 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    A.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett.B 242 (1990) 163 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev.D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].ADSMathSciNetGoogle Scholar
  31. [31]
    W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev.D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].ADSMathSciNetGoogle Scholar
  32. [32]
    W. Siegel, Manifest duality in low-energy superstrings, in International Conference on Strings 93, Berkeley, California, 24-29 May 1993, pp. 353-363 (1993) [hep-th/9308133] [INSPIRE].
  33. [33]
    C. Hull and B. Zwiebach, Double Field Theory, JHEP09 (2009) 099 [arXiv:0904.4664] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
  35. [35]
    B. Zwiebach, Double Field Theory, T-duality and Courant Brackets, Lect. Notes Phys.851 (2012) 265 [arXiv:1109.1782] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring Double Field Theory, JHEP06 (2013) 101 [arXiv:1304.1472] [INSPIRE].
  37. [37]
    O. Hohm, D. Lüst and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys.61 (2013) 926 [arXiv:1309.2977] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    O. Hohm, S.K. Kwak and B. Zwiebach, Double Field Theory of Type II Strings, JHEP09 (2011) 013 [arXiv:1107.0008] [INSPIRE].
  39. [39]
    Y. Sakatani, S. Uehara and K. Yoshida, Generalized gravity from modified DFT, JHEP04 (2017) 123 [arXiv:1611.05856] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    J.-i. Sakamoto, Y. Sakatani and K. Yoshida, Weyl invariance for generalized supergravity backgrounds from the doubled formalism, PTEP2017 (2017) 053B07 [arXiv:1703.09213] [INSPIRE].
  41. [41]
    D. Lüst and D. Osten, Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality, JHEP05 (2018) 165 [arXiv:1803.03971] [INSPIRE].
  42. [42]
    S. Demulder, F. Hassler and D.C. Thompson, Doubled aspects of generalised dualities and integrable deformations, JHEP02 (2019) 189 [arXiv:1810.11446] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    C. Klimčík and P. Ševera, Dual nonAbelian duality and the Drinfeld double, Phys. Lett.B 351 (1995) 455 [hep-th/9502122] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    C. Klimčík, Poisson-Lie T duality, Nucl. Phys. Proc. Suppl.46 (1996) 116 [hep-th/9509095] [INSPIRE].
  45. [45]
    F. Hassler, Poisson-Lie T-duality in Double Field Theory, arXiv:1707.08624 [INSPIRE].
  46. [46]
    R. Blumenhagen, F. Hassler and D. Lüst, Double Field Theory on Group Manifolds, JHEP02 (2015) 001 [arXiv:1410.6374] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  47. [47]
    R. Blumenhagen, P. du Bosque, F. Hassler and D. Lüst, Generalized Metric Formulation of Double Field Theory on Group Manifolds, JHEP08 (2015) 056 [arXiv:1502.02428] [INSPIRE].
  48. [48]
    F. Hassler, The Topology of Double Field Theory, JHEP04 (2018) 128 [arXiv:1611.07978] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys.B 153 (1979) 61 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  50. [50]
    J. Scherk and J.H. Schwarz, Spontaneous Breaking of Supersymmetry Through Dimensional Reduction, Phys. Lett.82B (1979) 60 [INSPIRE].
  51. [51]
    D. Geissbuhler, Double Field Theory and N = 4 Gauged Supergravity, JHEP11 (2011) 116 [arXiv:1109.4280] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  52. [52]
    G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP11 (2011) 052 [Erratum ibid.11 (2011) 109] [arXiv:1109.0290] [INSPIRE].
  53. [53]
    M. Graña and D. Marques, Gauged Double Field Theory, JHEP04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
  54. [54]
    A. Catal-Ozer, Duality Twisted Reductions of Double Field Theory of Type II Strings, JHEP09 (2017) 044 [arXiv:1705.08181] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  55. [55]
    A. Catal-Ozer, Lunin-Maldacena deformations with three parameters, JHEP02 (2006) 026 [hep-th/0512290] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  56. [56]
    E. Bergshoeff, R. Kallosh, T. Ortín, D. Roest and A. Van Proeyen, New formulations of D = 10 supersymmetry and D8-O8 domain walls, Class. Quant. Grav.18 (2001) 3359 [hep-th/0103233] [INSPIRE].
  57. [57]
    S. Mukai, Symplectic Structure of the Moduli Space of Sheaves on an Abelian or K3 Surface, Invent. Math.77 (1984) 101.ADSMathSciNetCrossRefGoogle Scholar
  58. [58]
    A. Catal-Ozer, Massive deformations of Type IIA theory within double field theory, JHEP02 (2018) 179 [arXiv:1706.08883] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  59. [59]
    I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS 5× S 5superstring, JHEP04 (2014) 153 [arXiv:1401.4855] [INSPIRE].Google Scholar
  60. [60]
    B. Hoare and A.A. Tseytlin, Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS 5σ-model, J. Phys.A 49 (2016) 494001 [arXiv:1609.02550] [INSPIRE].Google Scholar
  61. [61]
    R. Borsato and L. Wulff, Integrable Deformations of T -Dual σ Models, Phys. Rev. Lett.117 (2016) 251602 [arXiv:1609.09834] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    J.-i. Sakamoto, Y. Sakatani and K. Yoshida, Homogeneous Yang-Baxter deformations as generalized diffeomorphisms, J. Phys.A 50 (2017) 415401 [arXiv:1705.07116] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  63. [63]
    I. Bakhmatov, E. Ó Colgáin, M.M. Sheikh-Jabbari and H. Yavartanoo, Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT), JHEP06 (2018) 161 [arXiv:1803.07498] [INSPIRE].
  64. [64]
    J.-I. Sakamoto and Y. Sakatani, Local β-deformations and Yang-Baxter σ-model, JHEP06 (2018)147 [arXiv:1803.05903] [INSPIRE].
  65. [65]
    I. Bakhmatov and E.T. Musaev, Classical Yang-Baxter equation from β-supergravity, JHEP01 (2019) 140 [arXiv:1811.09056] [INSPIRE].
  66. [66]
    T. Araujo, I. Bakhmatov, E. Ó. Colgáin, J. Sakamoto, M.M. Sheikh-Jabbari and K. Yoshida, Yang-Baxter σ-models, conformal twists and noncommutative Yang-Mills theory, Phys. Rev. D95 (2017) 105006 [arXiv:1702.02861] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    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. A51 (2018) 235401 [arXiv:1705.02063] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  68. [68]
    A. Çatal Özer and S. Tunalı, Yang-Baxter Deformation as an O(d, d) Transformation, arXiv:1906.09053 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Mathematicsİstanbul Technical UniversityIstanbulTurkey

Personalised recommendations