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Constraints and field equations for ten dimensional super Yang-Mills theory

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Abstract

We give a complete proof of the equivalence between constraint equations and field equations for thed=10,N=1 supersymmetric Yang-Mills theory, a result proposed and partially proved recently by Witten [1]. Our approach explicitly reconstructs the superconnection satisfying the constraints from the on shell component fields. A key ingredient of the method is the choice of a suitable family of gauges, effectively eliminating all gauge dependence on anti-commuting co-ordinates. As a corollary, obtained by dimensional reduction, we also deduce the equivalence of constraints and field equations for thed=4,N=4 theory, as well as ford=6,N=2.

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References

  1. Witten, E.: Twistor-like transform in ten dimensions. Princeton preprint (May 1985), to appear in Nucl. Phys. B (1986)

  2. Witten, E.: An interpretation of classical Yang-Mills theory. Phys. Lett.77B, 394 (1978)

    Google Scholar 

  3. Sohnius, M.: Bianchi identities for supersymmetric gauge theories. Nucl. Phys.B136, 461 (1978)

    Google Scholar 

  4. Harnad, J., Hurtubise, J, Légaré, M., Shnider, S.: Constraint equations and field equations in supersymmetricN = 3 Yang-Mills theory. Nucl. Phys.B256, 609 (1985)

    Google Scholar 

  5. Wess, J.: Supersymmetric gauge theories. In: Unified Field Theories and Beyond, Proc. 5th Johns Hopkins Workshop, 5 (1981)

  6. Brink, L., Scherk, J., Schwarz, J.: Supersymmetric Yang-Mills theories. Nucl. Phys.B121, 77 (1977)

    Google Scholar 

  7. Siegel, W.: Superfields in higher-dimensional spacetime. Phys. Lett.80B, 220 (1979)

    Google Scholar 

  8. Howe, P. S., Sierra, G., Townsend, P. K.: Supersymmetry in six dimensions. Nucl. Phys.B221, 331 (1983)

    Google Scholar 

  9. Devchand, C.: Integrability on Lightlike Lines in Six Dimensional Superspace. Freiburg preprint (September 1985)

  10. Koller, J.: A six-dimensional superspace approach to extended superfields. Nucl. Phys.B222, 319 (1983)

    Google Scholar 

  11. See, e.g. Gates, S. J., Jr., Grisaru, M. T., Rocek, M., Siegel, W.: Superspace. Reading, MA.: Benjamin/Cummings, 1983

    Google Scholar 

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Authors and Affiliations

  1. Département de Mathématiques Appliquées, Ecole Polytechnique, Succ. “A”, C.P. 6079, H3C 3A7, Montréal, Qué, Canada

    J. Harnad

  2. Department of Mathematics, McGill University, Montreal, Canada

    S. Shnider

  3. Department of Mathematics, Ben Gurion University, 84105, Beersheva, Israel

    S. Shnider

Authors
  1. J. Harnad
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  2. S. Shnider
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Additional information

Communicated by A. Jaffe

Research supported in part by the National Science and Engineering Research Council of Canada and the Israel Ministry of Science

On leave of absence from: Department of Pure and Applied Mathematics, Stevens Institute of Technology, Hoboken NJ 07030, USA

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Harnad, J., Shnider, S. Constraints and field equations for ten dimensional super Yang-Mills theory. Commun.Math. Phys. 106, 183–199 (1986). https://doi.org/10.1007/BF01454971

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  • DOI: https://doi.org/10.1007/BF01454971

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