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There are a lot of supersymmetric theories, and, sometimes,in the Lagrangian, there are interacting terms between bosonic and fermionic degrees of freedom, and sometimes not. Why ?

For instance, for the basic chiral superfield without superpotential, there is no interaction, while for 11-D supergravity, there is an interaction term between the (bilinear expression of) gravitinos and the strength 4-form.

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    $\begingroup$ You can't really write a free action in a gravity theory since the metric determinant enters into the measure $\mathrm{d}^D x\sqrt{-g}$, so that would be why you couldn't consistently drop interaction terms in SUGRA. Beyond that it depends entirely on the motivation of the theory whether and what interactions you include or not. $\endgroup$
    – Michael
    Commented May 17, 2013 at 16:18

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