# Superstring Theory problem. Infinitesimal supersymmetry transofrmations

1. Oct 9, 2012

### B3NR4Y

1. The problem statement, all variables and given/known data
Let

\delta _{1} \, and \, \delta _{2}

be two infinitesimal sypersymmetry transformations on xμ compute

[\delta _{1}, \delta _{2} ]x^{μ}.

2. Relevant equations
The commutator is:

[\delta _{1}, \delta _{2} ]x^{μ}=\delta_{1}\delta_{2} x^{μ} - \delta_{2}\delta_{1} x^{μ}

3. The attempt at a solution
I am able to get the first term, but the second term trips me up

\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}

2. Oct 9, 2012

### 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.

3. Oct 9, 2012

### 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

[\delta_{1} , \delta{2}] x^{μ}

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