I have often seen a relationship being alluded to between these two theories but I am unable to find any literature which proves/derives/explains this relationship.

I guess in the condensed matter physics literature this is the "same" thing which is referred to when they say that one has propagating chiral bosons on the boundary of the manifold if there is a Chern-Simons theory defined in the interior("bulk")

Let me quote (with some explanatory modifications) from two papers two most important aspects of the relationship that is alluded to,

*"...It is well known that any Chern-Simons theory admits a boundary which carries a chiral WZW model; however these degrees of freedom are not topological (the partition function of Chern-Simons theory coupled to such boundary degrees of freedom depends on the conformal class of the metric on the boundary)..."**"...In general if the pure Chern-Simons theory (of group $G$) at level k is formulated on a Riemann furface then the number of zero-energy states equals the number of conformal blocks of the WZW model of $G$ at level $k' = k - \frac{h}{2}$ ($h=$the quadratic Casimir of G in the adjoint representation)..(and when the Riemann surface is a torus) the number of conformal blocks is equal to the number of representations of $\hat{G}$ at level $k'$.."*

- I would like to know of a reference(s) (hopefully pedagogical/introductory!) which explains/proves/derives the above two claims. (..I looked through various sections of the book by Toshitake Kohno on CFT which deals with similar stuff but I couldn't identity these there..may be someone could just point me to the section in that book which may be explains the above claims but may be in some different garb which I can't recognize!..)