A unitary structure for the graded quotient of conformal coblocks

In this thesis, the construction of conformal coblocks, the dual of the conformal blocks, and the WZW connection on it are explained from a special perspective. Next, a natural filtration on the conformal coblocks is introduced and the graded quotient with respect to it are taken. On this graded quotient, a connection and compatible unitary structure are introduced. It is argued that this connection can, in a certain sense, be regarded as a graded version of the WZW connection.