  We study a class of renormalization group flows on line defects that can be
described by a generalized free field with ordered planar contractions on the
line. They are realized, for example, in large $N$ gauge theories with matter
in the fundamental representation and arise generically in non-relativistic
CFTs. We analyze the flow exactly and compute the change in the $g$-function
between the UV and IR fixed points. We relate the result to the change in the
two-point function of the displacement operator and check the monotonicity of
the defect entropy along the flow analytically. Finally, we give a general
realization of this type of flow starting from the direct sum of the IR fixed
point and a trivial line. This type of defect renormalization group flow
parallels the well-studied case of double-trace flow.
