I am not sure if I recall all the ways for a symmetry to appear as some particle in a Quantum Field Theory. - The Lagrangian and the vacuum is invariant under the generators of a global symmetry/gauge group. Then the particles in the theory are classified according representations of such group, with all the elements in the same multiplet having equal mass, but... a) Are all the representations expected to appear, and b) is the representation of the generators, the fundamental representation, expected to appear? - The Lagrangian is invariant under a global gauge group but the vacuum is not. The broken generators then appear as Goldstone bosons, of spin zero. Are they always spin zero? What about the unbrogen generators. No clue of them? - The Lagrangian is invariant under a local gauge group. Then the generators appear as massless spin 1 bosons, under the fundamental representation of the group. - The Lagrangian is invariant under a local gauge group and the vacuum is not. The unbroken generators appear as massless spin 1, the broken generators as massive spin 1, all of them join in a fundamental representation of the group that nevertheless has different masses.