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Extended SUSY and superspace

Physics Asked on October 5, 2021

I am trying to understand how to construct an action using the superspace formalism for $mathcal N>1$. I have read that this is quite difficult to do, so let’s consider a simple example. Suppose I want to construct an action for $d=1$, $mathcal N=2$ supergravity with an $mathcal O(mathcal N=2)$ local symmetry. Such an action might describe a massless point-particle with spin $1$; see https://doi.org/10.1088/1742-6596/1208/1/012006.

Question: How do I construct such an action with off-shell SUSY using the superspace formalism?

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