  The generalized Wilson loop operator interpolating between the supersymmetric
and the ordinary Wilson loop in ${\cal N}=4$ SYM theory provides an interesting
example of renormalization group flow on a line defect: the scalar coupling
parameter $\zeta$ has a non-trivial beta function and may be viewed as a
running coupling constant in a 1d defect QFT. In this paper we continue the
study of this operator, generalizing previous results for the beta function and
Wilson loop expectation value to the case of an arbitrary representation of the
gauge group and beyond the planar limit. Focusing on the scalar ladder limit
where the generalized Wilson loop reduces to a purely scalar line operator in a
free adjoint theory, and specializing to the case of the rank $k$ symmetric
representation of $SU(N)$, we also consider a certain semiclassical limit where
$k$ is taken to infinity with the product $k\, \zeta^2$ fixed. This limit can
be conveniently studied using a 1d defect QFT representation in terms of $N$
commuting bosons. Using this representation, we compute the beta function and
the circular loop expectation value in the large $k$ limit, and use it to
derive constraints on the structure of the beta function for general
representation. We discuss the corresponding 1d RG flow and comment on the
consistency of the results with the 1d defect version of the F-theorem.
