Finite gauge transformations and geometry in double field theory

  • C. M. Hull
Open Access
Regular Article - Theoretical Physics


Recently proposed forms for gauge transformations with finite parameters in double field theory are discussed and problematic issues are identified. A new form for finite gauge transformations is derived that reveals the underlying gerbe structure and the close relationship with generalised geometry. The nature of generalised tensors is elucidated, and in particular it is seen that the presence of a constant metric with split signature does not restrict the doubled geometry, provided it is a generalised tensor rather than a conventional tensor.


Space-Time Symmetries String Duality Effective field theories 


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.


  1. [1]
    A. Giveon and M. Roček, Generalized duality in curved string backgrounds, Nucl. Phys. B 380 (1992) 128 [hep-th/9112070] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    T. Kugo and B. Zwiebach, Target space duality as a symmetry of string field theory, Prog. Theor. Phys. 87 (1992) 801 [hep-th/9201040] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    A. Dabholkar and C.M. Hull, Duality twists, orbifolds and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    S. Kachru, M.B. Schulz, P.K. Tripathy and S.P. Trivedi, New supersymmetric string compactifications, JHEP 03 (2003) 061 [hep-th/0211182] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    C.M. Hull, A Geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    C.M. Hull, Doubled Geometry and T-Folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    A. Dabholkar and C.M. Hull, Generalised T-duality and non-geometric backgrounds, JHEP 05 (2006) 009 [hep-th/0512005] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    C.M. Hull and R.A. Reid-Edwards, Flux compactifications of string theory on twisted tori, Fortsch. Phys. 57 (2009) 862 [hep-th/0503114] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    C.M. Hull and R.A. Reid-Edwards, Gauge symmetry, T-duality and doubled geometry, JHEP 08 (2008) 043 [arXiv:0711.4818] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    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
  14. [14]
    C.M. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].ADSMathSciNetGoogle Scholar
  16. [16]
    C.M. Hull and B. Zwiebach, The Gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    O. Hohm, C.M. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    O. Hohm, C.M. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    D.S. Berman and D.C. Thompson, Duality Symmetric String and M-theory, Phys. Rept. 566 (2015) 1 [arXiv:1306.2643] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  21. [21]
    O. Hohm, D. Lust and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys. 61 (2013) 926 [arXiv:1309.2977] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    O. Hohm and B. Zwiebach, Large Gauge Transformations in Double Field Theory, JHEP 02 (2013) 075 [arXiv:1207.4198] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    J.-H. Park, Comments on double field theory and diffeomorphisms, JHEP 06 (2013) 098 [arXiv:1304.5946] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    D.S. Berman, M. Cederwall and M.J. Perry, Global aspects of double geometry, JHEP 09 (2014) 066 [arXiv:1401.1311] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    G. Papadopoulos, Seeking the balance: Patching double and exceptional field theories, JHEP 10 (2014) 089 [arXiv:1402.2586] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    M. Cederwall, The geometry behind double geometry, JHEP 09 (2014) 070 [arXiv:1402.2513] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    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
  28. [28]
    A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry I: Type II Theories, JHEP 11 (2011) 091 [arXiv:1107.1733] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math.DG/0209099] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    M. Gualtieri, Generalized complex geometry, math.DG/0401221 [INSPIRE].
  31. [31]
    N. Hitchin, Lectures on generalized geometry, arXiv:1008.0973 [INSPIRE].
  32. [32]
    N. Hitchin, Brackets, forms and invariant functionals, math.DG/0508618 [INSPIRE].

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.The Blackett LaboratoryImperial College LondonLondonUnited Kingdom

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