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Superstring Theory problem. Infinitesimal supersymmetry transofrmations

  1. Oct 9, 2012 #1

    B3NR4Y

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    Gold Member

    1. The problem statement, all variables and given/known data
    Let
    \begin{equation}
    \delta _{1} \, and \, \delta _{2}
    \end{equation}
    be two infinitesimal sypersymmetry transformations on xμ compute
    \begin{equation}
    [\delta _{1}, \delta _{2} ]x^{μ}.
    \end{equation}


    2. Relevant 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}


    3. 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}
     
  2. jcsd
  3. Oct 9, 2012 #2

    dextercioby

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    Science Advisor
    Homework Helper

    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.
     
  4. Oct 9, 2012 #3

    B3NR4Y

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    Gold Member

    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
    [itex][\delta_{1},\delta_{2}]x^{μ}=\delta_{1}\delta_{2}x^{μ}-\delta_{2}\delta_{1}x^{μ}[/itex]
    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
     
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