# What is the way to express Yang-Mills symmetry groups without gauges?

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?

• After removing the gauge freedom, there is still a global $SU(3)$ symmetry, and that's what relates the different gluons. – knzhou Oct 30 '19 at 0:18
• @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? – zooby Oct 30 '19 at 0:20
• Related post by OP: physics.stackexchange.com/q/508368/2451 – Qmechanic Oct 30 '19 at 0:38