  We consider line defects in d-dimensional Conformal Field Theories (CFTs).
The ambient CFT places nontrivial constraints on Renormalization Group (RG)
flows on such line defects. We show that the flow on line defects is
consequently irreversible and furthermore a canonical decreasing entropy
function exists. This construction generalizes the g theorem to line defects in
arbitrary dimensions. We demonstrate our results in a flow between Wilson loops
in 4 dimensions.
