# Differences between Goldstone bosons and fermions

I have been looking into basic SUSY and SUGRA theory and have a question relating to Goldstinos (particles giving gravitinos mass).

Simply are these analogous to Goldstone bosons produced in the Goldstone model which is due to symmetries, not super-symmetries being broken.

So they are like the same mechanism but in a Super-symmetric sense, why are they needed because surely if SS is broken (and they are produced) there wouldn't need to be a pair of fermion to boson particles or would there?

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## 1 Answer

First, let us start with several corrections.

Goldstinos are generally not "particles giving gravitinos their mass". This is only the case in supersymmetric theories that include gravity – i.e. supergravity theories. In non-gravitational theories, there are no gravitons and gravitinos but there may still exist goldstinos. They don't give masses to anyone. All these statements have counterparts for Goldstone bosons and bosonic symmetries. When these symmetries are global, the Goldstone bosons are massless and aren't eaten by anyone. If the broken symmetries belong to the gauge symmetries, the Goldstone bosons are "eaten" by the gauge bosons that receive an extra polarization and masses because of the Goldstone bosons.

Second, Goldstone bosons or goldstinos follow from broken generators of Lie symmetries. Whenever a bosonic generator is broken, there is a bosonic Goldstone boson. Whenever a fermionic generator such as the supercharge generating supersymmetry is broken, there is a fermionic goldstino. This is the rule. The OP tried to find an excuse or exception of some sort why the rule should be ignored or violated but the excuse doesn't work, the logic is invalid, and the would-be exception doesn't exist.

Third, spontaneously broken supersymmetry – and more generally, spontaneously broken symmetry of any kind (and we always talk about spontaneous breaking when there are Goldstone bosons and goldstinos) – doesn't mean that there is no trace of the symmetry left afterwards. Quite on the contrary, the symmetry has many physical consequences even after it's spontaneously broken. After all, the existence of Goldstone bosons and/or goldstinos is among the consequences of the (broken) symmetry. Quite generally, the symmetry always gets restored at high enough energies. That's true for bosonic symmetries such as the electroweak symmetry as well as fermionic symmetries such as supersymmetry (well, it's the only possible fermionic symmetry).

At high enough energies, the (different, symmetry-violating) masses of the particles may be ignored (the mass is negligible relatively to the high energy) and the particles restore their membership in the multiplets i.e. representations of the symmetries (such as doublets of $SU(2)$ or the pairs of superpartners in SUSY). That's also why the symmetry breaking doesn't affect the number of particle species that may be extracted from high-energy experiments (well above the symmetry breaking scale).

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