A note on the CFT origin of the strong constraint of DFT

  • André Betz
  • Ralph Blumenhagen
  • Dieter Lüst
  • Felix RenneckeEmail author
Open Access


In double field theory, motivated by its field theoretic consistency, the level matching condition is generalized to the so-called strong constraint. In this note, it is investigated what the two-dimensional conformal field theory origin of this constraint is. Initially treating the left- and right-movers as independent, we compute the torus partition function as well as a generalized Virasoro-Shapiro amplitude. In non-compact directions the strong constraint arises from the factorization of the Virasoro-Shapiro amplitude over physical states as determined by the modular invariant partition function. From the same argument, along internal toroidal directions, no analogous constraint arises.


Conformal Field Models in String Theory String Duality Bosonic Strings 


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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.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett. B 242 (1990) 163 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE].ADSMathSciNetGoogle Scholar
  4. [4]
    C.M. Hull, A Geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    A. Dabholkar and C. Hull, Generalised T-duality and non-geometric backgrounds, JHEP 05 (2006) 009 [hep-th/0512005] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    C.M. Hull, Global aspects of T-duality, gauged σ-models and T-folds, JHEP 10 (2007) 057 [hep-th/0604178] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    C.M. Hull, Doubled Geometry and T-Folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    D.S. Berman and N.B. Copland, The String partition function in Hulls doubled formalism, Phys. Lett. B 649 (2007) 325 [hep-th/0701080] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    D.S. Berman, N.B. Copland and D.C. Thompson, Background Field Equations for the Duality Symmetric String, Nucl. Phys. B 791 (2008) 175 [arXiv:0708.2267] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    D.S. Berman and D.C. Thompson, Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions, Phys. Lett. B 662 (2008) 279 [arXiv:0712.1121] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].ADSMathSciNetGoogle Scholar
  12. [12]
    W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].ADSMathSciNetGoogle Scholar
  13. [13]
    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
  14. [14]
    O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    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
  16. [16]
    D.S. Berman and D.C. Thompson, Duality Symmetric String and M-theory, arXiv:1306.2643 [INSPIRE].
  17. [17]
    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
  18. [18]
    O. Hohm and S.K. Kwak, Frame-like Geometry of Double Field Theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  19. [19]
    O. Hohm and S.K. Kwak, Double Field Theory Formulation of Heterotic Strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 1111 (2011) 109] [arXiv:1109.0290] [INSPIRE].
  21. [21]
    D. Geissbühler, Double Field Theory and N = 4 Gauged Supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    M. Graña and D. Marques, Gauged Double Field Theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring Double Field Theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    J. Scherk and J.H. Schwarz, Dual Models for Nonhadrons, Nucl. Phys. B 81 (1974) 118 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    F. Hassler and D. Lüst, Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds, arXiv:1401.5068 [INSPIRE].
  26. [26]
    R. Blumenhagen, D. Lüst and S. Theisen, Basic concepts of string theory, Springer, Germany (2013).CrossRefzbMATHGoogle Scholar
  27. [27]
    C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    K.S. Narain, New Heterotic String Theories in Uncompactified Dimensions < 10, Phys. Lett. B 169 (1986) 41 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    Y. Michishita, Field redefinitions, T-duality and solutions in closed string field theories, JHEP 09 (2006) 001 [hep-th/0602251] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

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© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • André Betz
    • 1
  • Ralph Blumenhagen
    • 1
  • Dieter Lüst
    • 1
    • 2
  • Felix Rennecke
    • 1
    Email author
  1. 1.Max-Planck-Institut für Physik (Werner-Heisenberg-Institut)MünchenGermany
  2. 2.Arnold Sommerfeld Center for Theoretical PhysicsMünchenGermany

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