SpringerLink
Log in

Generalised geometry, eleven dimensions and E11

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

Abstract

We construct the non-linear realisation of E 11 and its first fundamental representation in eleven dimensions at low levels. The fields depend on the usual coordinates of space-time as well as two form and five form coordinates. We derive the terms in the dynamics that contain the three form and six form fields and show that when we restrict their field dependence to be only on the usual space-time we recover the correct self-duality relation. Should this result generalise to the gravity fields then the non-linear realisation is an extension of the maximal supergravity theory, as previously conjectured. We also comment on the connections between the different approaches to generalised geometry.

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
EUR 32.99 /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 includes VAT (Canada)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  ADS  MATH  Google Scholar 

  2. I. Schnakenburg and P. West, Kac-Moody symmetries of IIB supergravity, Phys. Lett. B 517 (2001) 421 [hep-th/0107181] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. P.C. West, E 11 origin of brane charges and U-duality multiplets, JHEP 08 (2004) 052 [hep-th/0406150] [INSPIRE].

    Article  ADS  Google Scholar 

  4. F. Riccioni and P.C. West, The E 11 origin of all maximal supergravities, JHEP 07 (2007) 063 [ar**v:0705.0752] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. F. Riccioni and P.C. West, E 11 -extended spacetime and gauged supergravities, JHEP 02 (2008) 039 [ar**v:0712.1795] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. F. Riccioni and P. West, Local E 11, JHEP 04 (2009) 051 [ar**v:0902.4678] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. F. Riccioni, D. Steele and P. West, The E 11 origin of all maximal supergravities: The Hierarchy of field-strengths, JHEP 09 (2009) 095 [ar**v:0906.1177] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

  9. A. Kleinschmidt and P.C. West, Representations of G+++ and the role of space-time, JHEP 02 (2004) 033 [hep-th/0312247] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. P.C. West, The IIA, IIB and eleven-dimensional theories and their common E 11 origin, Nucl. Phys. B 693 (2004) 76 [hep-th/0402140] [INSPIRE].

    Article  ADS  Google Scholar 

  11. P.P. Cook and P.C. West, Charge multiplets and masses for E 11, JHEP 11 (2008) 091 [ar**v:0805.4451] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. P.C. West, Hidden superconformal symmetry in M-theory, JHEP 08 (2000) 007 [hep-th/0005270] [INSPIRE].

    Article  ADS  Google Scholar 

  13. P.C. West, Very extended E 8 and A 8 at low levels, gravity and supergravity, Class. Quant. Grav. 20 (2003) 2393 [hep-th/0212291] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  14. V. Ogievetsky, Infinite-dimensional algebra of general covariance group as the closure of the finite dimensional algebras of conformal and linear groups, Nuovo Cim. 8 (1973) 988 [INSPIRE].

    MathSciNet  Google Scholar 

  15. A. Borisov and V. Ogievetsky, Theory of dynamical affine and conformal symmetries as the theory of the gravitational field, Theor. Math. Phys. 21 (1975) 1179 [Teor. Mat. Fiz. 21 (1974) 32] [INSPIRE].

    Article  Google Scholar 

  16. C. Hillmann, Generalized E 7(7) coset dynamics and D = 11 supergravity, JHEP 03 (2009) 135 [ar**v:0901.1581] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. C. Hillmann, E 7(7) and D = 11 supergravity, ar**v:0902.1509 [INSPIRE].

  18. P. West, Generalised space-time and duality, Phys. Lett. B 693 (2010) 373 [ar**v:1006.0893] [INSPIRE].

    ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  21. M. Duff, Duality rotations in string theory, Nucl. Phys. B 335 (1990) 610 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. M. Duff and J. Lu, Duality rotations in membrane theory, Nucl. Phys. B 347 (1990) 394 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. P.C. West, Brane dynamics, central charges and E 11, JHEP 03 (2005) 077 [hep-th/0412336] [INSPIRE].

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  27. C. Hull and B. Zwiebach, Double field theory, JHEP 09 (2009) 099 [ar**v:0904.4664] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. C. Hull and B. Zwiebach, The gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [ar**v:0908.1792] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [ar**v:1003.5027] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [ar**v:1006.4823] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. P. West, E 11 , generalised space-time and IIA string theory, Phys. Lett. B 696 (2011) 403 [ar**v:1009.2624] [INSPIRE].

    ADS  Google Scholar 

  32. A. Rocen and P. West, E 11 , generalised space-time and IIA string theory: the RR sector, ar**v:1012.2744 [INSPIRE].

  33. D.S. Berman and M.J. Perry, Generalized geometry and M-theory, JHEP 06 (2011) 074 [ar**v:1008.1763] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. 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 [ar**v:1103.5733] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  35. D.S. Berman, H. Godazgar, M.J. Perry and P. West, Duality invariant actions and generalised geometry, ar**v:1111.0459 [INSPIRE].

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

    Article  MathSciNet  MATH  Google Scholar 

  37. N. Hitchin, Brackets, forms and invariant functionals, math/0508618 [INSPIRE].

  38. M. Gualtieri, Generalized complex geometry, math/0401221 [INSPIRE].

  39. A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as generalised geometry I: type II theories, JHEP 11 (2011) 091 [ar**v:1107.1733] [INSPIRE].

    Article  ADS  Google Scholar 

  40. J.H. Schwarz and P.C. West, Symmetries and transformations of chiral N = 2 D = 10 supergravity, Phys. Lett. B 126 (1983) 301 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  41. P.S. Howe and P.C. West, The complete N = 2, D = 10 supergravity, Nucl. Phys. B 238 (1984) 181 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. J.H. Schwarz, Covariant field equations of chiral N = 2 D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [INSPIRE].

    Article  ADS  Google Scholar 

  43. I. Campbell and P.C. West, N = 2 D = 10 nonchiral supergravity and its spontaneous compactification, Nucl. Phys. B 243 (1984) 112 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. F. Giani and M. Pernici, N = 2 supergravity in ten-dimensions, Phys. Rev. D 30 (1984) 325 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  45. M. Huq and M. Namazie, Kaluza-Klein supergravity in ten-dimensions, Class. Quant. Grav. 2 (1985) 293 [Erratum ibid. 2 (1985) 597] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, King’s College, London, WC2R 2LS, UK

    Peter West

Authors
  1. Peter West
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter West.

Additional information

ArXiv ePrint: 1111.1642

Rights and permissions

Reprints and permissions

About this article

Cite this article

West, P. Generalised geometry, eleven dimensions and E11 . J. High Energ. Phys. 2012, 18 (2012). https://doi.org/10.1007/JHEP02(2012)018

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2012)018

Keywords

Search

Navigation