Renormalizability of pure $\mathcal{N}=1$ Super Yang-Mills in the Wess-Zumino gauge in the presence of the local composite operators $A^{2}$ and $\bar{\lambda}\lambda$

TL;DR

This paper proves the all-orders renormalizability of pure $ ext{N}=1$ Super Yang-Mills theory in the Wess-Zumino gauge with specific local composite operators, using algebraic renormalization techniques.

Contribution

It provides an all-orders proof of renormalizability for $ ext{N}=1$ Super Yang-Mills with local operators, identifying only three necessary renormalization constants.

Findings

Renormalizability holds at all orders with three renormalization constants.

The non-renormalization theorem for the gluon--ghost--anti-ghost vertex remains valid.

The gauge field and gluino have different renormalization factors due to non-linear supersymmetry.

Abstract

The renormalization of $\mathcal{N}=1$ Super Yang-Mills theory with the presence of the local composite operators $AA$, $A_\mu \gamma_\mu \lambda$ and $\bar{\lambda}\lambda$ is analyzed in the Wess-Zumino gauge, employing the Landau condition. An all-orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field, and gluino renormalization. The non-renormalization theorem of the gluon--ghost--anti-ghost vertex in the Landau gauge is shown to remain valid in $\mathcal{N}=1$ Super Yang-Mills with the presence of the local composite operators. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino.