# Massive Majorana fermions - nontrivial gauge multiplets?

1. Jan 22, 2014

### lpetrich

From supersymmetry, gauge particles have superpartners, gauginos. Supersymmetry breaking will make all the gauginos massive, since none have been observed. But that has certain problems.

A gauge field is a multiplet in its gauge group where each member corresponds to a generator of that group. That puts the field in the adjoint representation of that group. There's a theorem that states that that rep is always a real rep, so a gauge field can be real-valued instead of complex-valued without loss of generality. A gauge field is a massless vector field in the absence of the Higgs mechanism or anything similar, meaning that it has degrees of freedom corresponding to helicities +1 and -1.

By supersymmetry, each gauge-field generator has a corresponding gaugino mode with only two degrees of freedom. That makes gauginos Majorana fields, with helicities +1/2 and -1/2. Is that right about them?

If they get mass from SUSY breaking, that would make them massive Majorana fields.

Massive Majorana fields follow the Majorana equation - Wikipedia:
i*D(ψ) = m*ψc
where
ψ is the field, ψc is its charge conjugate, m is the mass, and D is the derivative operator γμ.Dμ

ψc = i*C.ψ*
where C is some matrix, the identity matrix in the Majorana basis.

At first sight, it seems as if a massive Majorana field cannot be in a nontrivial rep of a gauge group. But if the rep's group-element matrices are all real, then it becomes possible.

So a Majorana particle can be in any real rep of a gauge group. That includes the adjoint rep, meaning that massive Majorana gauginos are possible. Is that correct?