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Non-abelian T-duality and consistent truncations in type-II supergravity

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Abstract

For a general class of SO(4) symmetric backgrounds in type-II supergravity, we show that the action of non-Abelian T-duality can be described via consistent truncation to seven dimensional theories with seemingly massive modes. As such, any solution to these theories uplifts to both massive type IIA and IIB supergravities presenting an invertible map between the two. For supersymmetric backgrounds, we show that for spinors transforming under SO(4) the non-Abelian T-duality transformation breaks the original supersymmetry by half. We use these mappings to generate the non-Abelian T-duals of the maximally supersymmetric pp-wave, the Lin, Lunin, Maldacena geometries and spacetimes with Lifshitz symmetry.

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References

  1. B. Fridling and A. Jevicki, Dual representations and ultraviolet divergences in nonlinear σ-models, Phys. Lett. B 134 (1984) 70 [INSPIRE].

    Article  ADS  Google Scholar 

  2. E. Fradkin and A.A. Tseytlin, Quantum equivalence of dual field theories, Annals Phys. 162 (1985) 31 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. X.C. de la Ossa and F. Quevedo, Duality symmetries from non-abelian isometries in string theory, Nucl. Phys. B 403 (1993) 377 [hep-th/9210021] [INSPIRE].

    Article  ADS  Google Scholar 

  4. 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].

    Article  MathSciNet  ADS  Google Scholar 

  5. 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].

    Article  ADS  Google Scholar 

  6. E. Bergshoeff, C.M. Hull and T. Ortín, Duality in the type-II superstring effective action, Nucl. Phys. B 451 (1995) 547 [hep-th/9504081] [INSPIRE].

    Article  ADS  Google Scholar 

  7. H. Samtleben and M. Weidner, The maximal D = 7 supergravities, Nucl. Phys. B 725 (2005) 383 [hep-th/0506237] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].

    Article  ADS  Google Scholar 

  9. H. Lü, C. Pope and T.A. Tran, Five-dimensional N = 4, SU(2) × U(1) gauged supergravity from type IIB, Phys. Lett. B 475 (2000) 261 [hep-th/9909203] [INSPIRE].

    Article  ADS  Google Scholar 

  10. M. Cvetič, H. Lü, C. Pope, A. Sadrzadeh and T.A. Tran, Consistent SO(6) reduction of type IIB supergravity on S 5, Nucl. Phys. B 586 (2000) 275 [hep-th/0003103] [INSPIRE].

    Article  ADS  Google Scholar 

  11. A. Khavaev, K. Pilch and N.P. Warner, New vacua of gauged N = 8 supergravity in five-dimensions, Phys. Lett. B 487 (2000) 14 [hep-th/9812035] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. B. de Wit and H. Nicolai, The consistency of the S 7 truncation in D = 11 supergravity, Nucl. Phys. B 281 (1987) 211 [INSPIRE].

    Article  ADS  Google Scholar 

  13. H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistent nonlinear KK reduction of 11 − D supergravity on AdS 7 × S 4 and selfduality in odd dimensions, Phys. Lett. B 469 (1999) 96 [hep-th/9905075] [INSPIRE].

    Article  ADS  Google Scholar 

  14. H. Nastase, D. Vaman and P. van Nieuwenhuizen, Consistency of the AdS 7 × S 4 reduction and the origin of selfduality in odd dimensions, Nucl. Phys. B 581 (2000) 179 [hep-th/9911238] [INSPIRE].

    Article  ADS  Google Scholar 

  15. H. Nicolai and K. Pilch, Consistent truncation of D = 11 supergravity on AdS 4 × S 7, JHEP 03 (2012) 099 [arXiv:1112.6131] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. A.-K. Kashani-Poor, Nearly Kähler reduction, JHEP 11 (2007) 026 [arXiv:0709.4482] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. D. Cassani and A.-K. Kashani-Poor, Exploiting N = 2 in consistent coset reductions of type IIA, Nucl. Phys. B 817 (2009) 25 [arXiv:0901.4251] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. J.P. Gauntlett, S. Kim, O. Varela and D. Waldram, Consistent supersymmetric Kaluza-Klein truncations with massive modes, JHEP 04 (2009) 102 [arXiv:0901.0676] [INSPIRE].

    Article  ADS  Google Scholar 

  19. E. O Colgain, O. Varela and H. Yavartanoo, Non-relativistic M-theory solutions based on Kähler-Einstein spaces, JHEP 07 (2009) 081 [arXiv:0906.0261] [INSPIRE]

    Article  ADS  Google Scholar 

  20. E. O Colgain and H. Samtleben, 3D gauged supergravity from wrapped M 5-branes with AdS/CMT applications, JHEP 02 (2011) 031 (2011)031 [arXiv:1012.2145] [INSPIRE]

    Article  Google Scholar 

  21. D. Cassani, G. Dall’Agata and A.F. Faedo, Type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 05 (2010) 094 [arXiv:1003.4283] [INSPIRE]

    Article  MathSciNet  ADS  Google Scholar 

  22. K. Skenderis, M. Taylor and D. Tsimpis, A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure, JHEP 06 (2010) 025 [arXiv:1003.5657] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. J.P. Gauntlett and O. Varela, Universal Kaluza-Klein reductions of type IIB to N = 4 supergravity in five dimensions, JHEP 06 (2010) 081 [arXiv:1003.5642] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. J.T. Liu, P. Szepietowski and Z. Zhao, Consistent massive truncations of IIB supergravity on Sasaki-Einstein manifolds, Phys. Rev. D 81 (2010) 124028 [arXiv:1003.5374] [INSPIRE].

    ADS  Google Scholar 

  25. D. Cassani and P. Koerber, Tri-sasakian consistent reduction, JHEP 01 (2012) 086 [arXiv:1110.5327] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. I. Bah, A. Faraggi, J.I. Jottar, R.G. Leigh and L.A. Pando Zayas, Fermions and D = 11 supergravity on squashed Sasaki-Einstein manifolds, JHEP 02 (2011) 068 [arXiv:1008.1423] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. I. Bah, A. Faraggi, J.I. Jottar and R.G. Leigh, Fermions and type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 01 (2011) 100 [arXiv:1009.1615] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. M. Cvetič, H. Lü, C. Pope, A. Sadrzadeh and T.A. Tran, S 3 and S 4 reductions of type IIA supergravity, Nucl. Phys. B 590 (2000) 233 [hep-th/0005137] [INSPIRE].

    Article  ADS  Google Scholar 

  29. E. O Colgain and O. Varela, Consistent reductions from D = 11 beyond Sasaki-Einstein, Phys. Lett. B 703 (2011) 180 [arXiv:1106.4781] [INSPIRE].

    Article  ADS  Google Scholar 

  30. K. Sfetsos, Non-abelian duality, parafermions and supersymmetry, Phys. Rev. D54 (1996) 1682 [hep-th/9602179] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  31. S. Hassan, T duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [INSPIRE].

    Article  ADS  Google Scholar 

  32. M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, A new maximally supersymmetric background of IIB superstring theory, JHEP 01 (2002) 047 [hep-th/0110242] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP 08 (2010) 014 [arXiv:1005.3291] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. 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].

    Article  ADS  Google Scholar 

  36. A.H. Chamseddine and W. Sabra, D = 7 SU(2) gauged supergravity from D = 10 supergravity, Phys. Lett. B 476 (2000) 415 [hep-th/9911180] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. P. Townsend and P. van Nieuwenhuizen, Gauged seven-dimensional supergravity, Phys. Lett. B 125 (1983) 41 [INSPIRE].

    Article  ADS  Google Scholar 

  38. M. Cvetič, H. Lü and C. Pope, Consistent Kaluza-Klein sphere reductions, Phys. Rev. D 62 (2000) 064028 [hep-th/0003286] [INSPIRE].

    ADS  Google Scholar 

  39. A. Salam and E. Sezgin, SO(4) gauging of N = 2 supergravity in seven-dimensions, Phys. Lett. B 126 (1983) 295 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. J. Morales and H. Samtleben, Higher spin holography for SYM in d dimensions, Phys. Lett. B 607 (2005) 286 [hep-th/0411246] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. L. Romans, Gauged N = 4 supergravities in five-dimensions and their magnetovac backgrounds, Nucl. Phys. B 267 (1986) 433 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. M. Cvetič, H. Lü and C. Pope, Consistent warped space Kaluza-Klein reductions, half maximal gauged supergravities and CP n constructions, Nucl. Phys. B 597 (2001) 172 [hep-th/0007109] [INSPIRE].

    Article  ADS  Google Scholar 

  43. J.P. Gauntlett and O. Varela, D = 5 SU(2) × U(1) gauged supergravity from D = 11 supergravity, JHEP 02 (2008) 083 [arXiv:0712.3560] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. E. Alvarez, L. Álvarez-Gaumé, J. Barbon and Y. Lozano, Some global aspects of duality in string theory, Nucl. Phys. B 415 (1994) 71 [hep-th/9309039] [INSPIRE].

    Article  ADS  Google Scholar 

  45. A.P. Polychronakos and K. Sfetsos, High spin limits and non-abelian T-duality, Nucl. Phys. B 843 (2011) 344 [arXiv:1008.3909] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. Y. Kosmann, A note on Lie-Lorentz derivatives, Ann. Mat. Pura Appl. 91 (1972) 317.

    Article  MathSciNet  MATH  Google Scholar 

  47. J.M. Figueroa-O’Farrill, On the supersymmetries of Anti-de Sitter vacua, Class. Quant. Grav. 16 (1999) 2043 [hep-th/9902066] [INSPIRE]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. T. Ortín, A note on Lie-Lorentz derivatives, Class. Quant. Grav. 19 (2002) L143 [hep-th/0206159] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  49. A. Buchel, Coarse-graining 1/2 BPS geometries of type IIB supergravity, Int. J. Mod. Phys. A 21 (2006) 3495 [hep-th/0409271] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. M.M. Caldarelli, D. Klemm and P.J. Silva, Chronology protection in Anti-de Sitter, Class. Quant. Grav. 22 (2005) 3461 [hep-th/0411203] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. I. Bena and N.P. Warner, A harmonic family of dielectric flow solutions with maximal supersymmetry, JHEP 12 (2004) 021 [hep-th/0406145] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  53. A. Donos and J.P. Gauntlett, Lifshitz solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. P. Candelas and X.C. de la Ossa, Comments on conifolds, Nucl. Phys. B 342 (1990) 246 [INSPIRE].

    Article  ADS  Google Scholar 

  55. J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Sasaki-Einstein metrics on S 2 × S 3, Adv. Theor. Math. Phys. 8 (2004) 711 [hep-th/0403002] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  56. S.R. Das, J. Michelson, K. Narayan and S.P. Trivedi, Time dependent cosmologies and their duals, Phys. Rev. D 74 (2006) 026002 [hep-th/0602107] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  57. C. Burgess, N. Grandi, F. Quevedo and R. Rabadán, D-brane chemistry, JHEP 01 (2004) 067 [hep-th/0310010] [INSPIRE].

    ADS  Google Scholar 

  58. K.-M. Lee, E. O Colgain, H. Yavartanoo and K. Yogendran, BPS D0-D6 branes in supergravity, JHEP 03 (2009) 009 [arXiv:0811.2086] [INSPIRE]

    Article  ADS  Google Scholar 

  59. J.M. Maldacena and J.G. Russo, Large-N limit of noncommutative gauge theories, JHEP 09 (1999) 025 [hep-th/9908134] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  60. 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]

    Article  ADS  MATH  Google Scholar 

  61. D. Gaiotto and J. Maldacena, The gravity duals of N = 2 superconformal field theories, arXiv:0904.4466 [INSPIRE].

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Authors and Affiliations

  1. Department of Engineering Sciences, University of Patras, 26110, Patras, Greece

    Georgios Itsios & Konstadinos Sfetsos

  2. Centro de Fisica do Porto & Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal

    Georgios Itsios

  3. Department of Physics, University of Oviedo, Avda. Calvo Sotelo 18, 33007, Oviedo, Spain

    Yolanda Lozano & Eoin Ó Colgáin

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  1. Georgios Itsios
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  2. Yolanda Lozano
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  3. Eoin Ó Colgáin
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  4. Konstadinos Sfetsos
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Correspondence to Georgios Itsios.

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ArXiv ePrint: 1205.2274

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Itsios, G., Lozano, Y., Colgáin, E.Ó. et al. Non-abelian T-duality and consistent truncations in type-II supergravity. J. High Energ. Phys. 2012, 132 (2012). https://doi.org/10.1007/JHEP08(2012)132

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