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Given a Yang-Mills theory such as $SU(3)$ which has 8 gluons. After we gauge-fix this theory, it no longer has $SU(3)$ guage symmetry. Yet, we still use the group constants and the 8 types of gluons to calculate the Feynman graphs.

Thus the gauge-fixed action still retains some sort of $SU(3)$-ness to it even though it is not a local symmetry any more.

In the gauge-fixed action, what is the name of this $SU(3)$-ness?

It's like we start with a guage theory with group $G$, then gauge-fix it to remove the guage freedoms, but are left with a shadow of the group $G$.

i.e. we could still classify all gauge-fixed Yang-Mills actions by a group $G$.

So what is the relation of the gauge group to the gauge-fixed action?

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  • $\begingroup$ After removing the gauge freedom, there is still a global $SU(3)$ symmetry, and that's what relates the different gluons. $\endgroup$ – knzhou Oct 30 '19 at 0:18
  • $\begingroup$ @knzhou I see, so with gauge-fixing you are making the symmetry act in the same way for all points in space-time turning the local symmetry into a global symmetry? $\endgroup$ – zooby Oct 30 '19 at 0:20
  • $\begingroup$ Related post by OP: physics.stackexchange.com/q/508368/2451 $\endgroup$ – Qmechanic Oct 30 '19 at 0:38

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