Two AdS2 branes in the Euclidean AdS3

5 pages, some arguments clarified, version published in JHEPWe compute the density of open strings stretching between AdS2 branes in the Euclidean AdS3. This is done by solving the factorization constraint of a degenerate boundary field, and the result is checked by a Cardy-type computation. We mention applications to branes in the Minkowskian AdS3 and its cigar coset