The role of field redefinition on renormalisability of a general $N=\frac{1}{2}$ supersymmetric gauge theories

TL;DR

This paper examines how field redefinitions affect the renormalisability of non-anticommutative $N=1/2$ supersymmetric gauge theories, demonstrating that proper redefinitions ensure one-loop renormalisability and gauge invariance.

Contribution

It introduces a specific field redefinition approach that restores renormalisability in $N=1/2$ supersymmetric gauge theories with matter fields.

Findings

Proper field redefinitions are necessary for renormalisability.

The modified Lagrangian includes extra terms for renormalisation.

The theory remains gauge invariant up to one-loop corrections.

Abstract

We investigate some issues on renormalisability of non-anticommutative supersymmetric gauge theory related to field redefinitions. We study one loop corrections to $N=\frac{1}{2}$ supersymmetric $SU(N)\times U(1)$ gauge theory coupled to chiral matter in component formalism, and show the procedure which has been introduced for renormalisation is problematic because some terms which are needed for the renormalisability of theory are missed from the Lagrangian. In order to prove the theory is renormalisable, we redefine the gaugino and the auxiliary fields($\lambda, \bar F$), which result in a modified form of the Lagrangian in the component formalism. Then, we show the modified Lagrangian has extra terms which are necessary for renormalisability of non-anticommutative supersymmetric gauge field theories. Finally we prove $N = \frac{1}{2}$ supersymmetric gauge theory is renormalisable up to one loop corrections using standard method of renormalisation; besides, it is shown the effective action is gauge invariant.