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I was working through the Mirror Symmetry book by Clay Math Institute. It deals with supersymmetric sigma model in 10.4 section. It doesn't derive how the action is invariant under the variation. I am trying hard, but stuck at few places. Does any one have any references for such a calculations ? The Lagrangian and variation is given in the following image. I have given the lagrangian, if one doesn't have the soft copy of the book.

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Related question: physics.stackexchange.com/q/52462/2451 –  Qmechanic Feb 1 '13 at 17:29
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