Chern-Simons

It's a Schwartz type 2+1 d TQFT.

1. When the 3-manifold $W$ is closed (so that can perform as a boundary), its Lagrangian can be viewed as the second Chern class on the bulk manifold.
2. $W$ has a boundary: spatial slices/bdy corresponds to a CFT--gauged WZW model, captures behavior of CS under gauge transformation with certain boundary conditions; vertical Wilson loop~characters (operator map); wave functional~conformal blocks; Hilbert space are the same, whose dim counts theta functions (genus>0~non-Abelian); its genus 0 3-pt correlator~Verlinde formula, 2-pt~metric of chiral ring. This CS/WZW model duality is a kind of AdS\CFT correspondence.
   Give rise to $\varphi F$ theory after integrating out time/vertical/non-Abelian fields. Reduce to 2d Yang-Mills when coupling $e\to 0$. [hep-th/9312104] The Verlinde Algebra And The Cohomology Of The Grassmannian
   The Abelian CS theory can explain the fractional quantum Hall effect (FQHE).
   The configuration space is the moduli space of flat connections (so that labelled by Wilson loops), whose geometric quantization needs Kahler polarization. The expectations of Wilson loops in CS theory are Jones polynomials.
   The path integral of Chern-Simons theory on $W$ can also be realized by that of $\mathcal{N}=4$ super Yang-Mills theory on a half-space $V=W\times {\mathbb{R}}_{+}$, thus reduced from the string theory. (categorification)

3d $\mathcal{N}=2$ CS with fundamental chirals (furthermore, flavors) admits two IR phases: 3d $\mathcal{N}=2$ Grassmannian sigma model and pure CS. $\to$ correspondence between Verlinde algebra of WZW model & quantum cohomology of Grassmannian (reduce to WZW at long distances). [1302.2164v1] Wilson loops in supersymmetric Chern-Simons-matter theories and duality