Doubled Field Theory, T-Duality and Courant-Brackets

Part of the Lecture Notes in Physics book series (LNP, volume 851)


In these lecture notes we give a simple introduction into double field theory. We show that the presence of momentum and winding excitations in toroidal backgrounds of closed string theory makes it natural to consider double field theories. A tool-kit is developed based on the Courant-bracket and generalized Lie derivatives. We construct a background independent action which represents a T-duality covariantization of the Einstein-Hilbert action for gravity coupled to an antisymmetric tensor field and a dilaton.



I would like to thank the organizers of the International School for their invitation to lecture and for their hospitality. I am also grateful to Marco Baumgartl and Nicolas Moeller who prepared an excellent version of the lecture notes that was easy to edit and finalize. Finally, I thank Olaf Hohm for comments and suggestions on this draft.


  1. 1.
    Hull, C., Zwiebach, B.: Double field theory. JHEP 0909, 099 (2009). [arXiv:0904.4664 [hep-th]]Google Scholar
  2. 2.
    Hull, C., Zwiebach, B.: The gauge algebra of double field theory and courant-brackets. JHEP 0909, 090 (2009). [arXiv:0908.1792 [hep-th]]Google Scholar
  3. 3.
    Hohm, O., Hull, C., Zwiebach, B.: Background independent action for double field theory. JHEP 1007, 016 (2010). [arXiv:1003.5027 [hep-th]]Google Scholar
  4. 4.
    Hohm, O., Hull, C., Zwiebach, B.: Generalized metric formulation of double field theory. JHEP 1008, 008 (2010). [arXiv:1006.4823 [hep-th]]Google Scholar
  5. 5.
    Siegel, W.: Superspace duality in low-energy superstrings. Phys. Rev. D48, 2826–2837 (1993). [hep-th/9305073]Google Scholar
  6. 6.
    Siegel, W.: Two vierbein formalism for string inspired axionic gravity. Phys. Rev. D47, 5453–5459 (1993). [hep-th/9302036]Google Scholar
  7. 7.
    Tseytlin, A.A,: Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B350, 395–440 (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations