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arXiv · hep-th/9604146

Supersymmetry and Noncommutative Geometry

W. Kalau·M. Walze
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Abstract

The purpose of this article is to apply the concept of the spectral triple, the starting point for the analysis of noncommutative spaces in the sense of A.~Connes, to the case where the algebra $\cA$ contains both bosonic and fermionic degrees of freedom. The operator $\cD$ of the spectral triple under consideration is the square root of the Dirac operator und thus the forms of the generalized differential algebra constructed out of the spectral triple are in a representation of the Lorentz group with integer spin if the form degree is even and they are in a representation with half-integer spin if the form degree is odd. However, we find that the 2-forms, obtained by squaring the connection, contains exactly the components of the vector multiplet representation of the supersymmetry algebra. This allows to construct an action for supersymmetric Yang-Mills theory in the framework of noncommutative geometry.

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W. Kalau, M. Walze. 1996-04-23. Supersymmetry and Noncommutative Geometry. https://doi.org/10.1016/s0393-0440(96)00029-0

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