In this work we propose an exact microscopic description of maximally symmetric branes in a Euclidean AdS_3 background. As shown by Bachas and Petropoulos, the most important such branes are localized along a Euclidean AdS_2 ⊂ AdS_3. We provide explicit formulas for the coupling of closed strings to such branes (boundary states) and for the spectral density of open strings. The latter is computed in two different ways first in terms of the open string reflection amplitude and then also from the

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... boundary states by world-sheet duality. This gives rise to an important Cardy type consistency check. All the results are compared in detail with the geometrical picture. We also discuss a second class of branes with spherical symmetry and finally comment on some implications for D-branes in a 2D back hole geometry.