$n$-dimensional irreducible representation $R$, $\omega$ is an automorphism of the Lie algebra $g$, $\lambda$ and $\bar\lambda$ are independent real coupling constants, and there is an implicit sum over the adjoint index $a$. It will be useful to consider (\[basic\]) as the Wilson loop of a two-dimensional gauge field with components $$(\alpha_+,\alpha_-)\;=\; (\; \lambda\; J^a t^a\; ,\;
\bar\lambda\; \omega(\bar J^a)t^a\; )\  .$$ By virtue of the non-abelian Stokes theorem, the observables (\[basic\]) are conserved under the (closed-string) time evolution, provided that the field strength $F_{+-}= i\;[\alpha_+,\alpha_-]$ vanishes. This is however not the case in general, except for chiral (or antichiral) defects for which the coupling $\bar\lambda$ (or $\lambda$) is zero.

Let us concentrate on the chiral defects, with Wilson loops $$\label{bas}
{\cal O}_{\rm chir}(\lambda ; R ) =  {\rm Tr}_R\; {\rm P \; exp}
\;\left( i  \lambda \oint_C dx^+ \; J^a t^a \right)\ .$$ Classically, such Wilson loops are topological, [*i.e.*]{} they only depend on the homotopy class of the contour $C$. This property does not, a priori, survive the renormalisation process, which introduces through dimensional transmutation a length scale. There is however one special value of the coupling, $$\lambda^* = -{1\over \kappa}\ ,$$ for which ${\cal O}_{\rm chir}(\lambda^*; R)$ is 