Non-local Wess-Zumino Model on Nilpotent Noncommutative Superspace

Abstract

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.

arXiv commentLatex, 16 pages, 2 figures, typos corrected, some references and comments on auxiliary field added, a figure replaced, English refined

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• Chern-Simons-Matter Theory
• M-Theory on Deformed Superspace
• Deformation of the ABJM Theory
• The BV Formalization of Chern-Simons Theory on Deformed Superspace
• Gauged Wess-Zumino Model in Noncommutative Minkowski Superspace
• Nonlocal quantum field theory without acausality and nonunitarity at quantum level: is SUSY the key?
• Aspects of ABJ Theory
• Non-anticommutative ABJ Theory
• Field Theory on Nonanticommutative Superspace
• Drinfel'd Twisted Superconformal Algebra and Structure of Unbroken Symmetries
• Nonanticommutative Deformation of N=4 SYM Theory: The Myers Effect and Vacuum States
• Nilpotent noncommutativity and renormalization
• D-deformed Wess-Zumino model and its renormalizability properties
• Non-anticommutative Supersymmetric Field Theory and Quantum Shift
• N=1/2 Global SUSY: R-Matrix Approach