# Weak isospin and types of weak charge

My understanding is that QCD has three color charges that are conserved as a result of global SU(3) invariance. What about SU(2) weak? Does it have two types of charges? What I'm getting at is:

U(1) --> 1 type of charge

SU(2) --> ?

SU(3) --> 3 types of charge

Does SU(2) have two types? If not, what is the relation between SU(N) invariance and the number of charge types?

Idea: Maybe both I and I_3 (weak isospin and its third component) are conserved before electroweak symmetry breaking? Is that true? If so, then that would answer my question.

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Actually each of the symmetry generators commutes with the Hamiltonian and gives a conserved charge. For an SU(N) group the number of generators is $N^2 - 1$. The total number of generators in the SM is $1 + (2^2 - 1) + (3^2 -1) = 12$. –  Michael Brown Mar 14 at 13:41
@Michael Brown, I am aware that local invariance of SU(N) leads to N^2-1 gauge fields, however I think this is a different question from what I am asking. SU(3) has 8 gauge fields (quantized becomes 8 gluons), but 3 colors. 3 conserved charges, due to global invariance of SU(3), not local. –  user1247 Mar 14 at 13:54
Look up Noether's theorem again. There is a conserved current $j_\mu^A$ for every generator $T^A$ of the group, i.e. the currents live in the adjoint rep. Therefore there are $N^2 - 1$ conserved charges. The number of components in the fundamental rep is a different matter. For SU(N) that is $N$. –  Michael Brown Mar 14 at 14:45
@Michael Brown, I thought that color charge was conserved, and that SU(3) implied three such colors. Am I mistaken that the "3" colors are related to the "3" in SU(3), and that their conservation is related to Noether's theorem? Any help would be appreciated. –  user1247 Mar 14 at 15:24
@Michael Brown, we assign quarks to the fundamental rep of SU(3), so there are three colors. We call it color charge, and it is conserved. Gluons are not conserved. I'm confused why a gluon would be considered a conserved charge by Noether. The color is the conserved charge. –  user1247 Mar 14 at 15:46