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For ordinary spontaneously broken symmetries, you can demonstrate relations between S-matrix elements with a soft goldstone emission and another S-matrix element without the emission.

If I break SUSY I get Nambu-Goldstone fermions. Does there exist a relation between matrix elements with a soft goldstino emission and a matrix element without the emission? Basically, what is the complication because the soft particle is a fermion? References are also useful.

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Soft goldstino theorems? Sure, Goldstino has some illustrative references, like Uematsu & Zachos, available here, which has the Adler zeroes exhibited explicitly, without exciting deviations from the boson/pion case. Basically the underlying principles are the same, and goldstinos decouple at vanishing momenta.

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