Journal of High Energy Physics

, 2019:10 | Cite as

O(D, D) gauge fields in the T-dual string Lagrangian

  • Machiko HatsudaEmail author
  • Warren Siegel
Open Access
Regular Article - Theoretical Physics


We present the string Lagrangian with manifest T-duality. Not only zero-modes but also all string modes are doubled. The gravitational field is an O(D, D) gauge field. We give a Lagrangian version of the section condition for the gauge invariance which compensates the O(D, D) transformation from the gravitational field and the GL(2D) coordinate transformation. We also show the gauge invariance of the line element of the manifest T-duality space and the O(D, D) condition on the background. Different sections describe dual spaces.


String Duality Bosonic Strings Gauge Symmetry 


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]
    M.J. Duff, Duality Rotations in String Theory, Nucl. Phys. B 335 (1990) 610 [INSPIRE].
  2. [2]
    A.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett. B 242 (1990) 163 [INSPIRE].
  3. [3]
    A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [INSPIRE].
  4. [4]
    W. Siegel, Manifest duality in low-energy superstrings, in proceedings of the International Conference on Strings 93, Berkeley, California, U.S.A., 24-29 May 1993, pp. 353-363 [hep-th/9308133] [INSPIRE].
  5. [5]
    W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
  6. [6]
    W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
  7. [7]
    M. Poláček and W. Siegel, Natural curvature for manifest T-duality, JHEP 01 (2014) 026 [arXiv:1308.6350] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    M. Hatsuda, K. Kamimura and W. Siegel, Ramond-Ramond gauge fields in superspace with manifest T-duality, JHEP 02 (2015) 134 [arXiv:1411.2206] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    M. Hatsuda, K. Kamimura and W. Siegel, Superspace with manifest T-duality from type-II superstring, JHEP 06 (2014) 039 [arXiv:1403.3887] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    M. Poláček and W. Siegel, T-duality off shell in 3D Type II superspace, JHEP 06 (2014) 107 [arXiv:1403.6904] [INSPIRE].
  11. [11]
    M. Hatsuda, K. Kamimura and W. Siegel, Type II chiral affine Lie algebras and string actions in doubled space, JHEP 09 (2015) 113 [arXiv:1507.03061] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    M. Hatsuda, K. Kamimura and W. Siegel, Manifestly T-dual formulation of AdS space, JHEP 05 (2017) 069 [arXiv:1701.06710] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle 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]
    B. Zwiebach, Double Field Theory, T-Duality, and Courant Brackets, Lect. Notes Phys. 851 (2012) 265 [arXiv:1109.1782] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    D.S. Berman and D.C. Thompson, Duality Symmetric String and M-theory, Phys. Rept. 566 (2014) 1 [arXiv:1306.2643] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    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
  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]
    W. Siegel, Manifest Lorentz Invariance Sometimes Requires Nonlinearity, Nucl. Phys. B 238 (1984) 307 [INSPIRE].
  19. [19]
    W. Siegel, Fields, hep-th/9912205 [INSPIRE].
  20. [20]
    J. Berkeley, D.S. Berman and F.J. Rudolph, Strings and Branes are Waves, JHEP 06 (2014) 006 [arXiv:1403.7198] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    K. Morand and J.-H. Park, Classification of non-Riemannian doubled-yet-gauged spacetime, Eur. Phys. J. C 77 (2017) 685 [arXiv:1707.03713] [INSPIRE].
  22. [22]
    O. Hohm and B. Zwiebach, Large Gauge Transformations in Double Field Theory, JHEP 02 (2013) 075 [arXiv:1207.4198] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    T.H. Buscher, Path Integral Derivation of Quantum Duality in Nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE].
  24. [24]
    T.H. Buscher, A Symmetry of the String Background Field Equations, Phys. Lett. B 194 (1987) 59 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Physics Division, Faculty of MedicineJuntendo UniversityChibaJapan
  2. 2.KEK Theory Center, High Energy Accelerator Research OrganizationTsukubaJapan
  3. 3.C.N. Yang Institute for Theoretical PhysicsState University of New YorkStony BrookU.S.A.

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