Are there really any AdS2 branes in the Euclidean (or not) AdS3?

We do not find any AdS2 branes, neither in the H3+ WZNW model nor in the SL(2,R) WZNW model. We then reexamine the case of the branes that possess a su(2) symmetry: we speculate that they would have to live on the boundary of AdS3. This cannot be realized in an Euclidean spacetime, but in the SL(2,R) WZNW model by analytical continuation.