not only for those corresponding to integrable representations of the current algebra.[^9]

We end this section with some remarks. Firstly, the topological defect lines (\[topW\]) should ‘lift’ to the (spacelike) Wilson lines of the 3d Chern-Simons theory [@Felder:1999cv], but it is not clear whether a lift exists for the more general, non-topological defects. Second, the above loop observables define a classical (fusion) algebra, $${\cal O}_\omega(\lambda, \bar\lambda  ; R_1 )\;  
{\cal O}_\omega(\lambda, \bar\lambda  ; R_2 )
= \sum_{R\in R_1\otimes R_2}  {\cal O}_\omega(\lambda, \bar\lambda  ; R )\ ,$$ for any values of the coupling constants. It would be interesting to know whether this algebra structure survives at the quantum level. Finally, the symmetric defects discussed here form a special class, and do not exhaust all conformal defects of WZW models.

Regularised loop operators
==========================

As a first step towards quantising the defect lines of the previous section, we will now describe a regularisation scheme and write ${\cal O}_\omega^{\rm reg}(\lambda,\bar\lambda; R)$ as an operator in the enveloping algebra of the current algebras. We start by defining the regularised left-moving currents $$\label{jreg}
J_{\rm reg}^a(\sigma) = \sum_{n\in {\bf Z}} J^a_n\;  
e^{-in\sigma - |n| s/2} \,,$$ where $s$ is a short-distance cutoff, and the $J^n_a$ are 