Some remarks on D-branes in AdS₃

We investigate the relation between the algebraic construction of boundary states in AdS_3 and the target space analysis of D-branes and show the consistency of the two descriptions. We compute, in the semiclassical regime, the overlap of a localized closed string state with boundary states and identify the latter with D-branes wrapping conjugacy classes in AdS_3. The string partition function on the disk is shown to reproduce the spacetime DBI action. Other consistency checks are performed. We also comment on the role of the spectral flow symmetry of the underlying SL(2,R)/U(1) coset model in constructing D-branes that correspond to degenerate representations of SL(2,R).