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so apologies if this is a silly question...

In the type 1 see saw model we add extra Majorana fermions to our model. These fermions have to be total gauge singlets in order to have a Majorana mass term and thus trigger the see saw mechanism.

In a supersymmetric model we add gauge singlet superfields whose fermionic components are majorana. My question is regarding the scalar component of this superfield - is it real or complex?

I think it should be real as the superfield itself has to be a gauge singlet and thus the scalar field has no charge associated with it.

Yes? No? Thanks in advance

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A supersymmetric supermultiplet - that is, a set of fields that are related by supersymmetry transformations - must contain a equal number of fermionic and bosonic degrees of freedom.

A Majorana fermion has two (on-shell) degrees of freedom. The Majorana's supersymmetric scalar partner must, therefore, be a complex scalar with two degrees of freedom.

A complex scalar field can be neutral under a $U(1)$ symmetry. Because the $U(1)$ transformation, $$ \phi\to\exp(iq\theta)\phi, $$ makes no sense if $\phi$ is a real field, all real scalar fields are necessarily neutral under a $U(1)$ symmetry; however, not all scalar fields that are neutral under a $U(1)$ are necessarily real fields.

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OK that was a silly question! Thanks for clearing it up! –  user48983 Jun 7 at 8:54

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