Massive Majorana fermions - nontrivial gauge multiplets?

[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*ψ^c
where
ψ is the field, ψ^c is its charge conjugate, m is the mass, and D is the derivative operator γ^μ.D_μ

ψ^c = 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?

 

[AndyW]

I can confirm that your understanding of gauginos and their connection to supersymmetry is correct. Gauginos are the superpartners of gauge particles in supersymmetry, and their existence is predicted by this theory. However, as you mentioned, the fact that none have been observed poses a problem for supersymmetry.

Your explanation of the gauge field being in the adjoint representation and the corresponding gaugino having two degrees of freedom is also accurate. And yes, by supersymmetry, each gauge-field generator has a corresponding gaugino mode with helicities +1/2 and -1/2.

Regarding your question about mass and rep of a gauge group, you are correct that a massive Majorana field cannot be in a nontrivial rep of a gauge group. However, as you mentioned, if the rep's group-element matrices are all real, then it becomes possible for a Majorana particle to be in any real rep of a gauge group, including the adjoint rep. Therefore, it is possible for massive Majorana gauginos to exist.

In conclusion, your understanding of gauginos and their properties in relation to supersymmetry and gauge groups is correct. Keep exploring and asking questions, as these are important topics in the field of particle physics.