in fact invariant under the full symmetries (\[trans\]) of the WZW model. To see why, recall that a Wilson loop is invariant under the gauge transformations $$\alpha_\pm \to v^{-1}\alpha_\pm v - i v^{-1}\partial_\pm v$$ for arbitrary $v(x^+,x^-)$. The transformation (\[trans\]) of $\ (\lambda^* J^a t^a \;,\; 0)\ $ is of precisely this same form with $v(x^+,x^-)=u(x^+)$. An immediate consequence is that this special Wilson loop has vanishing Poisson brackets with both current algebras, $$\{ J_n^a\;,\; {\cal O}_{\rm chir}(\lambda^* ; R ) \}_{\;_{\rm PB}}
= \{ \bar J_n^a\;,\; 
{\cal O}_{\rm chir}(\lambda^* ; R )  \}_{\;_{\rm PB}} = 0\ .$$ As we will verify in the following sections, to lowest order in $1/\kappa$ these relations do survive the canonical correspondence $\{\; , \; \}_{\;_{\rm PB}} \to[\; , \; ]\ $ (though in general $\lambda^*$ has a finite, scheme-dependent renormalisation). Since the Virasoro generators are quadratic in the affine currents, ${\cal O}_{\rm chir}(\lambda^* ; R )$ will thus also obey eq. (\[topo\]) that characterises topological defects.

The above semiclassical argument can help us identify another class of defects, which are conformal but not topological. They correspond to the symmetric choice $$\lambda = \bar\lambda = {\lambda^*\over 2}\ .$$ With this choice, the observables (\[basic\]) 