Chern-Simons theory (say, with gauge group $G$) is the quantum theory of the Chern-Simons functional $$CS(A)=\frac{k}{8\pi^2}\int_M \text{Tr}\left(A\wedge dA + \frac{2}{3}A\wedge A \wedge A\right)$$ while instanton Floer homology is roughly the Morse homology of the moduli space of $G$-connections on $M$ with the Chern-Simons functional $CS(A)$ as Morse function.

Other than the superficial fact that they both use the Chern-Simons functional $CS(A)$ in some way, **is there any deeper connection between the Chern-Simons theory and the Floer homology?**

Added 10/11, just to clarify what I am asking :

There must be many different aspects of the connection between Chern-Simons theory and the Floer homology. For instance, let me list a few of what I've heard :

- (Kronheimer & Mrowka, 2010) For a link $K$, there is a spectral sequence whose $E_2$ page is the Khovanov homology of $K$ that abuts to the orbifold instanton homology $I^\natural (K)$.
- (Gukov, Putrov, Vafa) Both Heegaard Floer homology and Chern-Simons gauge theory arise naturally in the context of $6\text{d }\mathcal{N}=(0,2)$ SCFT.

I am interested in learning more about these connections, and also want to know other aspects of connection between CS theory and Floer theory; So I think my question is twofold : for one, I want a conceptual explanation of why the two theories should be related, and for two, I want to expand the above list of known facts revealing some deeper connection between the two theories.

Any comment is more than welcome.

notconsidered CS theory. $\endgroup$ – Henry Oct 11 '18 at 19:426more comments