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The superconformal algebra in higher dimensions

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Abstract

The superconformal algebra for 4/4N-dimensional super-Minkowski space (d=4) can be identified with the simple superalgebra su (2,2/N). For even-dimension d=5,6 the superconformal algebra can be identified with a real form of the simple superalgebras F(4), D(4,1) respectively in Kac's classification. For even-dimension d>-7 it is impossible to define a superconformal algebra satisfying three natural conditions: (1) it acts as infinitesimal automorphisms on super-Minkowski space; (2) this action extends the natural action of the super-Poincaré algebra; (3) when the action of the even part of the superconformal algebra is reduced to an infinitesimal action on ordinary Minkowski space, it extends the natural action of the conformal algebra so (2, d).

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References

  1. Cartan, E., The Theory of Spinors, Hermann, 1966, reissue, Dover, 1981.

  2. Chevalley, C., The Algebraic Theory of Spinors, Columbia University lectures.

  3. Finklestein, R. and Villasante, M., J. Math. Phys. 27, 1595 (1986).

    Google Scholar 

  4. Guillemin, V. and Sternberg, S., Bull. A.M.S. 70, 16 (1964).

    Google Scholar 

  5. Guillemin, V., J. Diff. Geom. 4, 257 (1970).

    Google Scholar 

  6. Harnad, J., Hurtubise, J., Legare, M., and Shnider, S., Nucl. Phys. B256, 609 (1985).

    Google Scholar 

  7. Harnad, J. and Shnider, S., Commun. Math. Phys. 106, 183 (1986).

    Google Scholar 

  8. Harnad, J. and Shnider, S., Isotropic geometry, twistors, and supertwistors I and II, preprint.

  9. Kac, V., Commun. Math. Phys. 53, 31 (1977).

    Google Scholar 

  10. Konstant, B., Graded manifolds, Springer Lecture Notes in Math. 570, 177.

  11. Manin, Y., Holomorphic supergeometry and Yang-Mills superfields, preprint.

  12. Singer, I. and Sternberg, S., J. Anal. Math. XV, 4.

  13. Van Holten, J. W. and Van Proeyen, A., J. Phys. A15, 3763 (1982).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University, Beersheva, Israel

    Steven Shnider

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  1. Steven Shnider
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Shnider, S. The superconformal algebra in higher dimensions. Lett Math Phys 16, 377–383 (1988). https://doi.org/10.1007/BF00402046

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  • DOI: https://doi.org/10.1007/BF00402046

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