Topological degree for supersymmetric chiral models

Matt Visser

doi:10.1103/PhysRevD.32.510

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Topological degree for supersymmetric chiral models

Matt Visser

Physics Department, University of California, Berkeley, California 94720

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Phys. Rev. D 32, 510 – Published 15 July, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.510

Abstract

For the case of an N-field supersymmetric chiral model we discuss the relationship between the Witten index, the topological degree, the winding number, and the degree of polynomials. Using results of classical analysis we can then place strong constraints on the Witten index of supersymmetric chiral models. For renormalizable chiral models, 2≤ $2^{\max}$ [n(m(z))]≤W≤ $2^{r (g ¯ g)}$ ≤ $2^{N}$ .

References (7)

J. Wess and J. Bagger, Supersymmetry and Supergravity (Princeton Univ. Press, Princeton, N.J., 1983).
E. Witten, Nucl. Phys. B202, 253 (1982).
S. Cecotti and L. Girardello, Phys. Lett. 110B, 39 (1982).
N. G. Lloyd, Degree Theory (Cambridge Univ. Press, Cambridge, 1978).
J. Cronin, Ann. Math. 58, 175 (1953); Proc. A. Math. Soc. 5, 175 (1954).
H. Nicolai, Ph.D. thesis, Universität Karlsruhe, 1975.
M. Visser (unpublished); B. Zumino (unpublished); J. Polchinski, Phys. Rev. D 27, 1320 (1983), Appendix A.

[c1] J. Wess and J. Bagger, Supersymmetry and Supergravity (Princeton Univ. Press, Princeton, N.J., 1983).

[c2] E. Witten, Nucl. Phys. B202, 253 (1982).

[c3] S. Cecotti and L. Girardello, Phys. Lett. 110B, 39 (1982).

[c4] N. G. Lloyd, Degree Theory (Cambridge Univ. Press, Cambridge, 1978).

[c5] J. Cronin, Ann. Math. 58, 175 (1953); Proc. A. Math. Soc. 5, 175 (1954).

[c6] H. Nicolai, Ph.D. thesis, Universität Karlsruhe, 1975.

[c7] M. Visser (unpublished); B. Zumino (unpublished); J. Polchinski, Phys. Rev. D 27, 1320 (1983), Appendix A.

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Topological degree for supersymmetric chiral models

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