  It is well-known that families of two-dimensional toroidal conformal field
theories possess a dense subset of rational toroidal conformal field theories,
which makes such families an interesting testing ground about rationality of
conformal field theories in families in general. Rational toroidal conformal
field theories possess an extended chiral and anti-chiral algebra known as
W-algebras. Their partition functions decompose into a finite sum of products
of holomorphic and anti-holomorphic characters of these W-algebras. Instead of
considering these characters, we decompose the partition functions into
products of characters of minimal extensions of $\widehat{\mathfrak{u}}(1)$
current algebras, which already appear for rational conformal field theories
with target space $S^1$. We present an explicit construction that determines
such decompositions. While these decompositions are not unique, they are
universal in the sense that any rational toroidal conformal field theory with a
target space torus of arbitrary dimension admits such decompositions. We
illustrate these decompositions with a few representative examples of rational
toroidal conformal field theories with two- and three-dimensional target space
tori.
