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Non-geometric branes are DFT monopoles

  • Ilya Bakhmatov
  • Axel Kleinschmidt
  • Edvard T. MusaevEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially on dual coordinates and have only trivial monodromies. Upon smearing the solutions along the dual coordinates one reproduces the known 5 2 2 solution for the Q-brane and co-dimension 1 solution for the R-brane. The T-duality invariant magnetic charge is explicitly calculated for all these backgrounds and is found to be equal to the magnetic charge of (unsmeared) NS5-brane.

Keywords

Solitons Monopoles and Instantons String Duality 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]
    O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    C. Hull and B. Zwiebach, Double field theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].ADSMathSciNetGoogle Scholar
  5. [5]
    D.S. Berman and D.C. Thompson, Duality symmetric string and M-theory, Phys. Rept. 566 (2014) 1 [arXiv:1306.2643] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    G. Aldazabal, D. Marques and C. Núñez, Double field theory: a pedagogical review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    C. Hull and B. Zwiebach, The gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP 01 (2013) 064 [arXiv:1208.5884] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    T.H. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    A. Dabholkar and C. Hull, Generalised T-duality and non-geometric backgrounds, JHEP 05 (2006) 009 [hep-th/0512005] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    C.M. Hull, Global aspects of T-duality, gauged σ-models and T-folds, JHEP 10 (2007) 057 [hep-th/0604178] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    C.M. Hull and R.A. Reid-Edwards, Non-geometric backgrounds, doubled geometry and generalised T-duality, JHEP 09 (2009) 014 [arXiv:0902.4032] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, Non-geometric fluxes in supergravity and double field theory, Fortsch. Phys. 60 (2012) 1150 [arXiv:1204.1979] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  18. [18]
    R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, A bi-invariant Einstein-Hilbert action for the non-geometric string, Phys. Lett. B 720 (2013) 215 [arXiv:1210.1591] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids, JHEP 02 (2013) 122 [arXiv:1211.0030] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    R. Blumenhagen, A. Deser, E. Plauschinn, F. Rennecke and C. Schmid, The intriguing structure of non-geometric frames in string theory, Fortsch. Phys. 61 (2013) 893 [arXiv:1304.2784] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  21. [21]
    D. Andriot and A. Betz, NS-branes, source corrected Bianchi identities and more on backgrounds with non-geometric fluxes, JHEP 07 (2014) 059 [arXiv:1402.5972] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    Y. Sakatani, Exotic branes and non-geometric fluxes, JHEP 03 (2015) 135 [arXiv:1412.8769] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  23. [23]
    M. Graña and D. Marqués, Gauged double field theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of double field theory, JHEP 11 (2011) 052 [Erratum ibid. 11 (2011) 109] [arXiv:1109.0290] [INSPIRE].
  25. [25]
    E.T. Musaev, Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions, JHEP 05 (2013) 161 [arXiv:1301.0467] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    D.S. Berman, E.T. Musaev, D.C. Thompson and D.C. Thompson, Duality invariant M-theory: gauged supergravities and Scherk-Schwarz reductions, JHEP 10 (2012) 174 [arXiv:1208.0020] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    W.H. Baron, Gaugings from E 7(7) extended geometries, Phys. Rev. D 91 (2015) 024008 [arXiv:1404.7750] [INSPIRE].ADSMathSciNetGoogle Scholar
  28. [28]
    G. Dibitetto, J.J. Fernandez-Melgarejo, D. Marques and D. Roest, Duality orbits of non-geometric fluxes, Fortsch. Phys. 60 (2012) 1123 [arXiv:1203.6562] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    J.A. Harvey and S. Jensen, Worldsheet instanton corrections to the Kaluza-Klein monopole, JHEP 10 (2005) 028 [hep-th/0507204] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    S. Jensen, The KK-monopole/NS5-brane in doubled geometry, JHEP 07 (2011) 088 [arXiv:1106.1174] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    J. Berkeley, D.S. Berman and F.J. Rudolph, Strings and branes are waves, JHEP 06 (2014) 006 [arXiv:1403.7198] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    D.S. Berman and F.J. Rudolph, Branes are waves and monopoles, JHEP 05 (2015) 015 [arXiv:1409.6314] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    D.S. Berman and F.J. Rudolph, Strings, branes and the self-dual solutions of exceptional field theory, JHEP 05 (2015) 130 [arXiv:1412.2768] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    T. Kimura and S. Sasaki, Gauged linear σ-model for exotic five-brane, Nucl. Phys. B 876 (2013) 493 [arXiv:1304.4061] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    T. Kimura and S. Sasaki, Worldsheet instanton corrections to 522 -brane geometry, JHEP 08 (2013) 126 [arXiv:1305.4439] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    J. de Boer and M. Shigemori, Exotic branes in string theory, Phys. Rept. 532 (2013) 65 [arXiv:1209.6056] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    T. Kimura, Semi-doubled σ-models for five-branes, JHEP 02 (2016) 013 [arXiv:1512.05548] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    D. Tong, NS5-branes, T duality and world sheet instantons, JHEP 07 (2002) 013 [hep-th/0204186] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    E.A. Bergshoeff, J. Hartong, T. Ortín and D. Roest, Seven-branes and supersymmetry, JHEP 02 (2007) 003 [hep-th/0612072] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    F. Hassler and D. Lüst, Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections, JHEP 07 (2013) 048 [arXiv:1303.1413] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    J.P. Gauntlett, J.A. Harvey and J.T. Liu, Magnetic monopoles in string theory, Nucl. Phys. B 409 (1993) 363 [hep-th/9211056] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    R. Gregory, J.A. Harvey and G.W. Moore, Unwinding strings and t duality of Kaluza-Klein and h monopoles, Adv. Theor. Math. Phys. 1 (1997) 283 [hep-th/9708086] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    N.A. Obers and B. Pioline, U duality and M-theory, Phys. Rept. 318 (1999) 113 [hep-th/9809039] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    E. Lozano-Tellechea and T. Ortín, 7-branes and higher Kaluza-Klein branes, Nucl. Phys. B 607 (2001) 213 [hep-th/0012051] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    F. Englert, L. Houart, A. Kleinschmidt, H. Nicolai and N. Tabti, An E 9 multiplet of BPS states, JHEP 05 (2007) 065 [hep-th/0703285] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  47. [47]
    A. Kleinschmidt, Counting supersymmetric branes, JHEP 10 (2011) 144 [arXiv:1109.2025] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    T. Ortín, Gravity and strings, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2015).Google Scholar
  49. [49]
    E.A. Bergshoeff, V.A. Penas, F. Riccioni and S. Risoli, Non-geometric fluxes and mixed-symmetry potentials, JHEP 11 (2015) 020 [arXiv:1508.00780] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  50. [50]
    V. Penas, Properties of double field theory, Ph.D. thesis, Groningen U., Groningen The Netherlands (2016).Google Scholar
  51. [51]
    D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring double field theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    C.D.A. Blair, Conserved currents of double field theory, JHEP 04 (2016) 180 [arXiv:1507.07541] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    J.-H. Park, S.-J. Rey, W. Rim and Y. Sakatani, O(D, D) covariant Noether currents and global charges in double field theory, JHEP 11 (2015) 131 [arXiv:1507.07545] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  54. [54]
    D.S. Berman, E.T. Musaev and M.J. Perry, Boundary terms in generalized geometry and doubled field theory, Phys. Lett. B 706 (2011) 228 [arXiv:1110.3097] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    U. Naseer, Canonical formulation and conserved charges of double field theory, JHEP 10 (2015) 158 [arXiv:1508.00844] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  56. [56]
    A. Giveon, E. Rabinovici and G. Veneziano, Duality in string background space, Nucl. Phys. B 322 (1989) 167 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    C.D.A. Blair, Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds, JHEP 06 (2015) 091 [arXiv:1405.2283] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  58. [58]
    O. Aharony, M. Berkooz, D. Kutasov and N. Seiberg, Linear dilatons, NS five-branes and holography, JHEP 10 (1998) 004 [hep-th/9808149] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    M. Graña, R. Minasian, M. Petrini and D. Waldram, T-duality, generalized geometry and non-geometric backgrounds, JHEP 04 (2009) 075 [arXiv:0807.4527] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  60. [60]
    D. Geissbuhler, Double field theory and N = 4 gauged supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Ilya Bakhmatov
    • 1
  • Axel Kleinschmidt
    • 2
    • 3
  • Edvard T. Musaev
    • 1
    • 2
    Email author
  1. 1.Kazan Federal University, Institute of Physics, General Relativity DepartmentKazanRussia
  2. 2.Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)PotsdamGermany
  3. 3.International Solvay InstitutesBruxellesBelgium

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