A Consistent Noncommutative Field Theory: the Wess-Zumino Model
H. O. Girotti, M. Gomes, V. O. Rivelles, A. J. da Silva
TL;DR
This paper demonstrates that the noncommutative Wess-Zumino model remains renormalizable at all perturbation orders due to supersymmetry, despite initial non-renormalizability of its scalar potential, and avoids problematic divergences.
Contribution
It shows that supersymmetry ensures the renormalizability of the noncommutative Wess-Zumino model, resolving issues with the scalar potential and IR/UV mixing.
Findings
The model is renormalizable to all orders.
Supersymmetry improves the scalar potential's renormalizability.
No quadratic or linear divergences are present.
Abstract
We show that the noncommutative Wess-Zumino model is renormalizable to all orders of perturbation theory. The noncommutative scalar potential by itself is non-renormalizable but the Yukawa terms demanded by supersymmetry improve the situation turning the theory into a renormalizable one. As in the commutative case, there are neither quadratic nor linear divergences. Hence, the IR/UV mixing does not give rise to quadratic infrared poles.
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