N=1 SUSY: How Many Superpartners for a Boson/Fermion?

[Femto]

I am sorry if the question is naive. In N=1 SUSY, for every boson we have a fermionic partner (and an auxilliary field) and vice-versa. When N>1 how many superpartners do we have given a boson (or a fermion)? Is it N?

 

[blechman]

N is the number of fermions in a given multiplet (for linearly realized SUSY, but that's a technicality).

Ex: for N=2, there are 2 (Weyl) fermions and therefore 4 (onshell) fermionic degrees of freedom. therefore you can either have 2 complex scalar fields (called a "Hypermultiplet"), or 1 complex scalar field and one massless gauge field (called a "Vector Multiplet") to make it supersymmetric.

etc.