Superstring Theory problem. Infinitesimal supersymmetry transofrmations

[B3NR4Y]

Homework Statement

Let
\begin{equation}
\delta _{1} \, and \, \delta _{2}
\end{equation}
be two infinitesimal sypersymmetry transformations on x^μ compute
\begin{equation}
[\delta _{1}, \delta _{2} ]x^{μ}.
\end{equation}

Homework Equations

The commutator is:
\begin{equation}
[\delta _{1}, \delta _{2} ]x^{μ}=\delta_{1}\delta_{2} x^{μ} - \delta_{2}\delta_{1} x^{μ}
\end{equation}

The Attempt at a Solution

I am able to get the first term, but the second term trips me up
\begin{equation}
\begin{split}
\delta_{1}\delta_{2} &= \delta_{1}( i\bar{\epsilon}^{A}_{2} \Gamma^{μ}\theta^{A})\\
& =i\bar{\epsilon}^{A}_{2} \Gamma^{μ}\delta_{2} \theta^{A}\\
& =i\bar{\epsilon}^{A}_{2} \Gamma^{μ}\theta^{A}
\end{split}
\end{equation}

 

[dextercioby]

It would be helpful if you told us what book/lecture notes you are reading, so we could get an idea on what the heck you're trying to do.

 

[B3NR4Y]

I'm working from the book 'String Theory Demystified' apparently, answers are not given (or were torn out by the previous person to own it). It asked me to compute
\begin{equation}
[\delta_{1} , \delta{2}] x^{μ}
\end{equation}
It then told me that the commutator was [δ1,δ2]xμ=δ1δ2xμ−δ2δ1xμ
[\delta_{1},\delta_{2}]x^{μ}=\delta_{1}\delta_{2}x^{μ}-\delta_{2}\delta_{1}x^{μ}
I'm trying to compute the second term, but I can't seem to do it. I already computed the first term in the original post