Advertisement

Spinors, Supergravity and the Signature of Space-Time

  • Ferrara S. 
Conference paper

Abstract

Supersymmetry algebras embedding space-time in any dimension and signature are considered. Different real forms of the R-symmetries arise both for usual space-time signature (one time) and for Euclidean or exotic signatures (more than one times). Application of these superalgebras are found in the context of supergravities with 32 supersymmetries, in any dimension D ≤ 11. These theories are related to D = 11, M, M * and M′ theories or D = 10, IIB, IIB* theories when compactified on Lorentzian tori. All dimensionally reduced theories fall in three distinct phases specified by the number of (128 bosonic) positive and negative norm states: (n +, n -) = (128, 0), (64, 64), (72, 56). 10D super Yang-Mills theories in (9,1) and (5,5) space-times are also considered, yielding N = 4, D = 4 gauge theories with (3,1), (4,0) and (2,2) signature.

Keywords

Spinor Representation Real Form Superconformal Algebra NucL Phys Supersymmetry Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D’Auria, R., Ferrara, S., Lledó, M.A., Varadarajan, VS.: hep-th/0010124Google Scholar
  2. 2.
    D’Auria, R., Ferrara, S., Lledó, M.A.: Embedding of space-time groups in simple superalgebras. CERN preprint CERN-TH/2000-380; Ferrara, S.: Letter in Math. Phys.; hep-th/0012186Google Scholar
  3. 3.
    Hull, C. (1998): JHEP 9807, 021; hep-th/9807127MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Cremmer, E., Lavrinenko, I.V., Lu, H., Pope, C.N., Stelle, K.S., Tran, T.A. (1998): Nucl. Phys. B 534, 40; hep-th/9803259MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Hull, C., Julia, B. (1998): Nucl. Phys. 534, 250MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Hull, C., Khuri, R. (1998): Nucl Phys. B 536, 219; hep-th/9808069; (2000): Nucl. Phys. B 575, 251; hep-th/9911082MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Moore, G.: hep-th/9305139Google Scholar
  8. 8.
    Hull, C. (1998): Nucl. Phys. B 536, 219; hep-th/9806146MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Ferrara, S., Günaydin, M. (1998): Int. J. Mod. Phys. A 13, 2075ADSMATHCrossRefGoogle Scholar
  10. 10.
    Ferrara, S., Maldacena, J. (1998): Class. Quant. Grav. 15, 749MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    Lu, H., Pope, C., Stelle, K.S. (1998): Class. Quant. Grav. 15, 537MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Chevalley, C. (1954): The algebraic theory of spinors. Columbia University PressGoogle Scholar
  13. 13.
    Bourbaki, N. (1958): Algèbre. Ch. 9, Hermann, ParisGoogle Scholar
  14. 14.
    Choquet-Bruhat, Y., DeWitt-Morette, C. (1989): Analysis, manifols and physics. Part II, Applications. North-Holland, AmsterdamGoogle Scholar
  15. 15.
    Deligne, P. (1999): Notes on Spinors, in Quantum Fields and Strings: A Course for Mathematicians, American Mathematical SocietyGoogle Scholar
  16. 16.
    Helgason, S. (1978): Differential geometry, Lie groups and symmetric spaces. Academic Press, New YorkMATHGoogle Scholar
  17. 17.
    Nahm, W. (1978): Nucl. Phys. B 135, 149ADSCrossRefGoogle Scholar
  18. 18.
    Van Proeyen, A.: hep-th/9910030Google Scholar
  19. 19.
    Nahm, W., Rittenberg, V, Scheunert, M. (1976): J. Math. Phys. 21, 1626MathSciNetGoogle Scholar
  20. 20.
    Kac, V.G. (1977): Commun. Math. Phys. 53, 31; Kac, V.G. (1977): Adv. Math. 26, 8; Kac, V.G. (1980): J. Math. Phys. 21, 689ADSMATHCrossRefGoogle Scholar
  21. 21.
    Parker, M. (1980): J. Math. Phys. 21, 689MathSciNetADSMATHCrossRefGoogle Scholar
  22. 22.
    D’Auria, R., Fré, P. (1982): Nucl. Phys. B 201, 101ADSCrossRefGoogle Scholar
  23. 23.
    van Holten, J.W., van Proeyen, A. (1982): J. Phys. A 15, 3763MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    Bergshoeff, E., van Proeyen, A.: hep-th/0003261, hep-th/0010194, hep-th/OO 10195Google Scholar
  25. 25.
    Bars, I. (2000): Phys. Rev. D 62, 046007; (1997): Phys. Lett. B 403, 257-264; (1997): Phys. Rev. D 55 2373-2381MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    Günaydin, M. (1998): Nucl. Phys. B 528, 432ADSMATHCrossRefGoogle Scholar
  27. 27.
    West, P. (2000): JHEP 0008, 007ADSCrossRefGoogle Scholar
  28. 28.
    Günaydin, M., Marcus, N. (1985): Class. Qaunt. Grav. 2, 219CrossRefGoogle Scholar
  29. 29.
    Hull, C.: JHEP 0012.007.2000, hep-th/0011215Google Scholar
  30. 30.
    Schwarz, J.H.: hep-th/0009009Google Scholar
  31. 31.
    Ferrara, S., Sokatchev, E.: hep-th/0005151Google Scholar
  32. 32.
    Gilmore, L. ( 1974): In Lie group, Lie algebras, and some of their applications. John Wiley & Sons, New York, Table 9.7Google Scholar
  33. 33.
    Siegel, W. (1992): Phys. Rev. D 46 3235; hep-th/9205075; (1993):Phys. Rev. D 47, 2504; hep-th/9207043; (1995):Phys. Rev. D 521 1042MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    McKeon, D.G.C. (2000): Can. J. Phys. 78, 261; McKeon, D.G.C, Sherry, T.M. (2000): Ann. Phys. 285, 221; hep-th/9810118; McKeon, D.G.C. (2000): Nucl. Phys. B 591, 591; Brandt, F.J., McKeon, D.G.C. (2000): Mod. Phys. Lett. A 15, 1349ADSCrossRefGoogle Scholar
  35. 35.
    Belitsky, A.V., Vandoren, S., van Nieuwenhuizen, P. (2000): Phys. Lett. B 477, 335; hep-th/0001010MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2002

Authors and Affiliations

  1. 1.Theoretical Physics Division, CERNGeneva 23Switzerland

Personalised recommendations