$\mathcal{N}=\frac{1}{2}$ Wess-Zumino Model Is Renormalizable

The Wess-Zumino model on $\mathcal{N}=\frac{1}{2}$ nonanticommutative superspace, which contains the dimension-6 term $F^3$, is shown to be renormalizable to all orders in perturbation theory, upon adding $F$ and $F^2$ terms to the original Lagrangian. The renormalizability is possible, even with this higher-dimension operator, because the Lagrangian is not Hermitian. Such deformed field theories arise naturally in string theory with a graviphoton background.

Figure 1

It is demonstrated how $\overline{A}{F}^2$ is related to $F^2$ by the insertion and deletion operations.