There are two facts I have heard about Chern-Simons theories
- They are dual to a WZW theory on the boundary (e.g. Relation between CS/WZW and AdS/CFT).
- They require a chiral theory on the boundary due to the requirements of gauge invariance. (e.g. Anomaly inflow mechanism)
The latter notion of the boundary theory has relevance to the edge modes in the quantum hall effect.
How are these two ideas relating 2+1d Chern-Simons to a 1+1d theory compatible? Are they the same? Is the theory in point 1 also chiral (corresponding to only including the holomorphic sector)? Is the theory in point 2 coupled to the gauge field (which I don't believe is the case for point 1)?
