Skip to main content
SpringerLink
Log in

Double field theory of type II strings

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

Abstract

We use double field theory to give a unified description of the low energy limits of type IIA and type IIB superstrings. The Ramond-Ramond potentials fit into spinor representations of the duality group O(D, D) and field-strengths are obtained by acting with the Dirac operator on the potentials. The action, supplemented by a Spin+ (D, D)-covariant self-duality condition on field strengths, reduces to the IIA and IIB theories in different frames. As usual, the NS-NS gravitational variables are described through the generalized metric. Our work suggests that the fundamental gravitational variable is a hermitian element of the group Spin(D, D) whose natural projection to O(D, D) gives the generalized metric.

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

Access this article

Log in via an institution

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. J. Polchinski, String theory, volume 2. Cambridge University Press, Cambridge U.K. (1998) [SPIRES].

    Book  Google Scholar 

  2. O. Hohm, S.K. Kwak and B. Zwiebach, Unification of type II strings and T-duality, arXiv:1106.5452 [SPIRES].

  3. M. Dine, P.Y. Huet and N. Seiberg, Large and small radius in string theory, Nucl. Phys. B 322 (1989) 301 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  5. E. Bergshoeff, C.M. Hull and T. Ortín, Duality in the type-II superstring effective action, Nucl. Phys. B 451 (1995) 547 [hep-th/9504081] [SPIRES].

    Article  ADS  Google Scholar 

  6. S.F. Hassan, SO(d, d) transformations of Ramond-Ramond fields and space-time spinors, Nucl. Phys. B 583 (2000) 431 [hep-th/9912236] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  7. S.F. Hassan, T-duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  8. M. Cvetič, H. Lü, C.N. Pope and K.S. Stelle, T-duality in the Green-Schwarz formalism and the massless/massive IIA duality map, Nucl. Phys. B 573 (2000) 149 [hep-th/9907202] [SPIRES].

    ADS  Google Scholar 

  9. B. Kulik and R. Roiban, T-duality of the Green-Schwarz superstring, JHEP 09 (2002) 007 [hep-th/0012010] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  10. I.A. Bandos and B. Julia, Superfield T-duality rules, JHEP 08 (2003) 032 [hep-th/0303075] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  11. R. Benichou, G. Policastro and J. Troost, T-duality in Ramond-Ramond backgrounds, Phys. Lett. B 661 (2008) 192 [arXiv:0801.1785] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  12. K.A. Meissner and G. Veneziano, Symmetries of cosmological superstring vacua, Phys. Lett. B 267 (1991) 33 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  13. K.A. Meissner and G. Veneziano, Manifestly O(d, d) invariant approach to space-time dependent string vacua, Mod. Phys. Lett. A 6 (1991) 3397 [hep-th/9110004] [SPIRES].

    ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  17. O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  18. O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  23. S.K. Kwak, Invariances and equations of motion in double field theory, JHEP 10 (2010) 047 [arXiv:1008.2746] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  24. O. Hohm and S.K. Kwak, Frame-like geometry of double field theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  25. O. Hohm, T-duality versus gauge symmetry, Prog. Theor. Phys. Suppl. 188 (2011) 116 [arXiv:1101.3484] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  26. O. Hohm, On factorizations in perturbative quantum gravity, JHEP 04 (2011) 103 [arXiv:1103.0032] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  27. O. Hohm and S.K. Kwak, Double field theory formulation of heterotic strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [SPIRES].

    Article  ADS  Google Scholar 

  28. D.S. Berman and M.J. Perry, Generalized geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [SPIRES].

    Article  ADS  Google Scholar 

  29. D.S. Berman, H. Godazgar and M.J. Perry, SO(5, 5) duality in M-theory and generalized geometry, Phys. Lett. B 700 (2011) 65 [arXiv:1103.5733] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  30. P. West, E 11 , generalised space-time and IIA string theory, Phys. Lett. B 696 (2011) 403 [arXiv:1009.2624] [SPIRES].

    ADS  Google Scholar 

  31. A. Rocen and P. West, E 11 , generalised space-time and IIA string theory: the RR sector, arXiv:1012.2744 [SPIRES].

  32. I. Jeon, K. Lee and J.-H. Park, Differential geometry with a projection: application to double field theory, JHEP 04 (2011) 014 [arXiv:1011.1324] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  33. I. Jeon, K. Lee and J.-H. Park, Double field formulation of Yang-Mills theory, Phys. Lett. B 701 (2011) 260 [arXiv:1102.0419] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  34. I. Jeon, K. Lee and J.-H. Park, Stringy differential geometry, beyond Riemann, Phys. Rev. D 84 (2011) 044022 [arXiv:1105.6294] [SPIRES].

    ADS  Google Scholar 

  35. N.B. Copland, Connecting T-duality invariant theories, arXiv:1106.1888 [SPIRES].

  36. D. Andriot, M. Larfors, D. Lüst and P. Patalong, A ten-dimensional action for non-geometric fluxes, arXiv:1106.4015 [SPIRES].

  37. D.C. Thompson, Duality invariance: from M-theory to double field theory, arXiv:1106.4036 [SPIRES].

  38. M. Fukuma, T. Oota and H. Tanaka, Comments on T-dualities of Ramond-Ramond potentials on tori, Prog. Theor. Phys. 103 (2000) 425 [hep-th/9907132] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  39. D. Brace, B. Morariu and B. Zumino, T-duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B 549 (1999) 181 [hep-th/9811213] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  40. D. Brace, B. Morariu and B. Zumino, Dualities of the matrix model from T-duality of the type-II string, Nucl. Phys. B 545 (1999) 192 [hep-th/9810099] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  41. C.M. Hull, Timelike T-duality, de Sitter space, large-N gauge theories and topological field theory, JHEP 07 (1998) 021 [hep-th/9806146] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  42. M. Gualtieri, Generalized complex geometry, Ph.D. thesis, Oxford University, Oxford U.K. (2004) [math.DG/0401221] [SPIRES].

  43. W. Fulton and J. Harris, Representation theory: a first course, Springer Verlag Inc., New York U.S.A. (1991).

    MATH  Google Scholar 

  44. E. Bergshoeff, R. Kallosh, T. Ortín, D. Roest and A. Van Proeyen, New formulations of D = 10 supersymmetry and D8-O8 domain walls, Class. Quant. Grav. 18 (2001) 3359 [hep-th/0103233] [SPIRES].

    Article  MATH  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  46. P.C. West, E 11 and M-theory, Class. Quant. Grav. 18 (2001) 4443 [hep-th/0104081] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  47. P.C. West, E 11 , SL(32) and central charges, Phys. Lett. B 575 (2003) 333 [hep-th/0307098] [SPIRES].

    ADS  Google Scholar 

  48. T. Damour, M. Henneaux and H. Nicolai, E 10 and a ‘small tension expansion’ of M-theory, Phys. Rev. Lett. 89 (2002) 221601 [hep-th/0207267] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  49. A. Kleinschmidt and H. Nicolai, E 10 and SO(9, 9) invariant supergravity, JHEP 07 (2004) 041 [hep-th/0407101] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, 02139, U.S.A.

    Olaf Hohm, Seung Ki Kwak & Barton Zwiebach

Authors
  1. Olaf Hohm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seung Ki Kwak
    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: 1107.0008

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hohm, O., Kwak, S.K. & Zwiebach, B. Double field theory of type II strings. J. High Energ. Phys. 2011, 13 (2011). https://doi.org/10.1007/JHEP09(2011)013

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP09(2011)013

Keywords

Search

Navigation