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-order multiplicative renormalizability of pure $ ext{N}=1$ Super Yang-Mills theory in the Wess-Zumino gauge with local composite operators, highlighting differences in renormalization factors due to supersymmetry realization.

Contribution

It provides the first all-order proof of renormalizability for the theory with specific composite operators in the Wess-Zumino gauge, considering supersymmetry's non-linear realization.

Findings

The theory is multiplicatively renormalizable at all orders.

The gauge field and gluino renormalization factors differ due to supersymmetry.

Composite operators are consistently incorporated into the renormalization framework.

Abstract

The $\mathcal{N}=1$ Super Yang-Mills theory in the presence of the local composite operator $A^2$ is analyzed in the Wess-Zumino gauge by employing the Landau gauge fixing condition. Due to the superymmetric structure of the theory, two more composite operators, $A_\mu \gamma_\mu \lambda$ and $\bar{\lambda}\lambda$, related to the susy variations of $A^2$ are also introduced. A BRST invariant action containing all these operators is obtained. An all order proof of the multiplicative renormalizability of the resulting theory is then provided by means of the algebraic renormalization setup. Though, 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.