Renormalization of supersymmetric gauge theory in the uneliminated component formalism

We show that the renormalization of the $\mathcal{N}=1$ supersymmetric gauge theory when working in the component formalism, without eliminating auxiliary fields and using a standard covariant gauge, requires a nonlinear renormalization of the auxiliary fields.

Figure 1

Diagrams with one $F$, two scalar lines. Dashed, full, double full, wavy, full/wavy, zigzag lines represent $\varphi$, $\psi$, $F$, $A$, $\lambda$, $D$ propagators, respectively.

Figure 2

Diagrams with one $D$, two scalar lines.

Figure 3

Diagrams with 2 $\varphi$, 2 $\overline{\varphi }$ lines and 2 or 4 Yukawa vertices.

Figure 4

Diagrams with 2 $\varphi$, 2 $\overline{\varphi }$ lines and 4 gauge vertices.