Non-local Wess-Zumino Model on Nilpotent Noncommutative Superspace

TL;DR

This paper studies a deformed Wess-Zumino model with bosonic-fermionic noncommutativity, revealing new interactions, supersymmetry breaking, and finite quantum corrections due to nilpotent couplings.

Contribution

It introduces a nilpotent noncommutative deformation of the Wess-Zumino model linking space-time and superspace noncommutativity, with explicit analysis of its effects.

Findings

Supersymmetry is fully broken to N=0 in Minkowski space.

The model includes new Grassmann-coupled interaction terms.

Finite noncommutative corrections occur at each loop order due to nilpotency.

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.