  We constrain renormalization group flows from $ABCDE$ type Wess-Zumino-Witten
models triggered by adjoint primaries. We propose positive Lagrangian coupling
leads to massless flow and negative to massive. In the conformal phase, we
prove an interface with the half-integral condition obeys the double braiding
relations. Distinguishing simple and non-simple flows, we conjecture the former
satisfies the half-integral condition. If the conjecture is true, some
previously allowed massless flows are ruled out. For $A$ type, known mixed
anomalies fix the ambiguity in identifications of Verlinde lines; an object is
identified with its charge conjugate. In the massive phase, we compute ground
state degeneracies.
