flow, then so is ${\cal O}_{\rm top} {|\!|}{\cal B}{\rangle\!\rangle}\to {\cal O}_{\rm top} {|\!|}{\cal B}^\prime{\rangle\!\rangle}$ for any topological-defect operator. This observation gives support for the flows that have been proposed in [@FS1; @Fredenhagen:2003xf].

Simple examples of topological defect operators are the generators of continuous symmetries, ${\cal O}_{\rm top}  = {\rm exp}(i\lambda\oint J)$ with $\lambda$ a real parameter and $J$ any abelian chiral spin-$1$ current. Another set includes discrete automorphisms of the CFT, as analyzed in ref. [@Frohlich:2004ef]. Both of these types of operators are invertible, and do not arise as infrared fixed points of RG flows, in contrast to the Kondo problem operators that we will study here.

Semiclassical analysis of WZW defects
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One may identify conformal defects in the WZW model by a semiclassical argument, analogous to the one used to argue for the existence of a conformal theory in the bulk [@Witten:ar]. We recall the expressions for the left- and right-moving currents of the model, $$J(x^+)  = -i \kappa\; (\partial_+  g)  g^{-1} \ \ \ {\rm and} \ \ \ \
\bar J(x^-) =   i \kappa\;  g^{-1}\partial_- g \ ,$$ where $x^\pm = \tau\pm\sigma$, and $g(x^+,x^-)$ takes values in some (simple compact) Lie group $G$. The parameter $\kappa$ 