Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-05-02
Phys.Rev. D72 (2005) 065015
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 16 pages, 2 figures, typos corrected, some references and comments on auxiliary field added, a figure replaced, English
Scientific paper
10.1103/PhysRevD.72.065015
We investigate the theory of the bosonic-fermionic noncommutativity, $[x^{\mu},\theta^{\alpha}] = i \lambda^{\mu \alpha}$, and the Wess-Zumino model deformed by the noncommutativity. Such noncommutativity links well-known space-time noncommutativity to superspace non-anticommutativity. The deformation has the nilpotency. We can explicitly evaluate noncommutative effect in terms of new interactions between component fields. The interaction terms that have Grassmann couplings are induced. The noncommutativity does completely break full $\mathcal{N}=1$ supersymmetry to $ \mathcal{N} = 0 $ theory in Minkowski signature. Similar to the space-time noncommutativity, this theory has higher derivative terms and becomes non-local theory. However this non-locality is milder than the space-time noncommutative field theory. Due to the nilpotent feature of the coupling constants, we find that there are only finite number of Feynman diagrams that give noncommutative corrections at each loop order.
Kobayashi Yoshishige
Sasaki Shin
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