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Massive Majorana fermions  nontrivial gauge multiplets? 
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#1
Jan2214, 01:31 AM

P: 530

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 realvalued instead of complexvalued 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 gaugefield 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 groupelement 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? 


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