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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?

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  • $\begingroup$ I think this counting is implicit in ed Witten paper, qft and the jones polynomial $\endgroup$ – ggcg Sep 24 '19 at 20:32

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