**Can the Yang-Mills or Chern-Simons action functionals be considered as [possibly *perfect*] Morse functions?** I assume we would be in an equivariant scenario due to considering the configuration spaces with gauge-groups/transformations. Or at least how far away are they from a Morse-Bott function (and from being perfect)?



Yang-Mills and Chern-Simons functionals as Morse functions
The problem with the CS functional is that the Morse indices of its critical points are infinite. In particular, this functional cannot be perfect. The Floer complex does not compute the homology of any particular space (though it might compute the homology of a certain spectrum).


On 4-manifolds the YM functional has some analytic deficiencies: it lacks Palais-Smale condition. This lack of Palais-Smale manifests itself in the form of "bubbling" which is a nagging issue to be taken seriously when defining Donaldson invariants.


On 2-manifolds it was investigated thoroughly by Atiyah-Bott. In that paper they describe how equivariant cohomology can be used to establish some forms of perfectness.


