One-loop renormalization of general $\mathcal{N}=\frac{1}{2}$ supersymmetric gauge theory

We investigate the one-loop renormalizability of a general $\mathcal{N}=\frac{1}{2}$ supersymmetric gauge theory coupled to chiral matter, and show the existence of an $\mathcal{N}=\frac{1}{2}$ supersymmetric $SU(N)\otimes U(1)$ theory which is renormalizable at one loop.

Figure 1

Diagrams with one gauge, two gaugino lines; the dot represents the position of a $C$.

Figure 2

Diagrams with two gauge and two gaugino lines; the dot represents the position of a $C$.

Figure 3

Diagrams with four gaugino lines; the dot represents the position of a $C$ or $|C{|}^2$.

Figure 4

Diagrams with one gaugino, one scalar and one chiral fermion line; the dot represents the position of a $C$.

Figure 5

Diagrams with one gaugino, one scalar, one chiral fermion and one gauge line; the dot represents the position of a $C$.

Figure 6

Diagrams with one gauge, one scalar and one auxiliary line; the dot represents the position of a $C$.

Figure 7

Diagrams with two gauge, one scalar and one auxiliary line; the dot represents the position of a $C$.

Figure 8

Diagrams with two gaugino, one scalar and one auxiliary line; the dot represents the position of a $C$ or a $|C{|}^2$.