On conformal field theories based on Takiff superalgebras

We revisit the construction of conformal field theories based on Takiff algebras and superalgebras that was introduced by Babichenko and Ridout. Takiff superalgebras can be thought of as truncated current superalgebras with $Z$-grading which arise from taking p copies of a Lie superalgebra $g$ and placing them in the degrees $s=0,\dots ,p-1$. Using suitably defined non-degenerate invariant forms we show that Takiff superalgebras give rise to families of conformal field theories with central charge $c=psdimg$. The resulting conformal field theories are defined in the standard way, i.e. they lend themselves to a Lagrangian description in terms of a WZW model and their chiral energy momentum tensor is the one obtained naturally from the usual Sugawara construction. In view of their intricate representation theory they provide interesting examples of conformal field theories. (paper)