Supertranslation

A supertranslation is generated by translations and supercharges, excluding the Lorentz transformations. For flat Majorana superspace with ${\Pi }^m=d{X}^m+i\bar{\theta }{\gamma }^{m}d\theta$, the rigid odd transformation $\delta \theta =ϵ$, $\delta X^m=-i\overline{ϵ}{\gamma }^m\theta$ leaves ${\Pi }^m$ invariant. Its commutator gives an ordinary translation.