For degrees of freedom (dof)
it is said that spin-1 massless boson like photon has 2 dof in 4d, like U(1) gauge theory.
it is said that spin-2 massless boson like photon has 2 dof in 4d, like Einstein gravity theory.
Can we demonstrate the following dof counting of gauge bosons of the gauge theories:
What is the dof of 3d Chern-Simons theory?
What is the dof of 4d SU(n) non-abelian gauge theory?
What is the dof of any d-dim Einstein gravity of spin-2 bosons?