Skip to main content
Springer Nature Link
Log in

Background independent action for double field theory

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. The gauge algebra is governed by the Courant bracket in certain subsectors of this double field theory. We construct the associated nonlinear background-independent action that is T-duality invariant and realizes the Courant gauge algebra. The action is the sum of a standard action for gravity, antisymmetric tensor, and dilaton fields written with ordinary derivatives, a similar action for dual fields with dual derivatives, and a mixed term that is needed for gauge invariance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Kugo and B. Zwiebach, Target space duality as a symmetry of string field theory, Prog. Theor. Phys. 87 (1992) 801 [hep-th/9201040] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  2. C. Hull and B. Zwiebach, Double field theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. C. Hull and B. Zwiebach, The gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  4. A.A. Tseytlin, Duality symmetric formulation of string world sheet dynamics, Phys. Lett. B 242 (1990) 163 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  5. A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [SPIRES].

    ADS  Google Scholar 

  7. W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [SPIRES].

    ADS  Google Scholar 

  8. B. Zwiebach, Closed string field theory: quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. T. Courant, Dirac manifolds, Trans. Amer. Math. Soc. 319 (1990) 631.

    Article  MATH  MathSciNet  Google Scholar 

  10. N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math/0209099]. = MATH/0209099;

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Gualtieri, Generalized complex geometry, Ph.D. thesis, Oxford Univeristy, Oxford U.K. (2004), math/0401221.

  12. Z.-J. Liu, A. Weinstein, and P. Xu, Manin triples for Lie bialgebroids, J. Diff. Geom. 45 (1997) 547 [math/9508013].

    MathSciNet  Google Scholar 

  13. M. Gualtieri, Branes on Poisson varieties, arXiv:0710.2719.

  14. A. Giveon, E. Rabinovici and G. Veneziano, Duality in string background space, Nucl. Phys. B 322 (1989) 167 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. A.D. Shapere and F. Wilczek, Selfdual models with theta terms, Nucl. Phys. B 320 (1989) 669 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. Y. Michishita, Field redefinitions, T-duality and solutions in closed string field theories, JHEP 09 (2006) 001 [hep-th/0602251] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. T. Damour, S. Deser and J.G. McCarthy, Nonsymmetric gravity theories: inconsistencies and a cure, Phys. Rev. D 47 (1993) 1541 [gr-qc/9207003] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  19. A.A. Tseytlin, σ-model approach to string theory, Int. J. Mod. Phys. A 4 (1989) 1257 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. J. Polchinski, String theory. Vol. 1: an introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998).

    Google Scholar 

  21. C.M. Hull and R.A. Reid-Edwards, Gauge symmetry, T-duality and doubled geometry, JHEP 08 (2008) 043 [arXiv:0711.4818] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. C.M. Hull and R.A. Reid-Edwards, Non-geometric backgrounds, doubled geometry and generalised T-duality, JHEP 09 (2009) 014 [arXiv:0902.4032] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. C.M. Hull, Doubled geometry and T-folds, JHEP 07 (2007) 080 [hep-th/0605149] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. C.M. Hull, Generalised geometry for M-theory, JHEP 07 (2007) 079 [hep-th/0701203] [SPIRES].

    Article  ADS  Google Scholar 

  26. P.P. Pacheco and D. Waldram, M-theory, exceptional generalised geometry and superpotentials, JHEP 09 (2008) 123 [arXiv:0804.1362] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. J. Maharana and J.H. Schwarz, Noncompact symmetries in string theory, Nucl. Phys. B 390 (1993) 3 [hep-th/9207016] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  28. E. Cremmer and B. Julia, The SO(8) supergravity, Nucl. Phys. B 159 (1979) 141 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. B. de Wit and H. Nicolai, Hidden symmetries, central charges and all that, Class. Quant. Grav. 18 (2001) 3095 [hep-th/0011239] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  30. C.C. Chevalley, The algebraic theory of spinors, Columbia University Press, U.S.A. (1954).

    MATH  Google Scholar 

  31. E. Artin, Geometric algebra, Interscience Publishers Inc., U.S.A. (1957).

    MATH  Google Scholar 

  32. T.H. Buscher, A symmetry of the string background field equations, Phys. Lett. B 194 (1987) 59 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  33. T.H. Buscher, Path integral derivation of quantum duality in nonlinear sigma models, Phys. Lett. B 201 (1988) 466 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  34. A. Giveon and M. Roček, Generalized duality in curved string backgrounds, Nucl. Phys. B 380 (1992) 128 [hep-th/9112070] [SPIRES].

    Article  ADS  Google Scholar 

  35. C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  36. C. Hillmann, Generalized E(7(7)) coset dynamics and D = 11 supergravity, JHEP 03 (2009) 135 [arXiv:0901.1581] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.

    Olaf Hohm & Barton Zwiebach

  2. The Blackett Laboratory, Imperial College London, Prince Consort Road, London, SW7 @AZ, U.K.

    Chris Hull

Authors
  1. Olaf Hohm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chris Hull
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Barton Zwiebach
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olaf Hohm.

Additional information

ArXiv ePrint: 1003.5027

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hohm, O., Hull, C. & Zwiebach, B. Background independent action for double field theory. J. High Energ. Phys. 2010, 16 (2010). https://doi.org/10.1007/JHEP07(2010)016

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP07(2010)016

Keywords

Search

Navigation