A Defect in AdS3/CFT2 Duality

$Ad{S}_3$ string theory in the stringy regime $k=(R_{AdS}\mathrm{/}{\mathrm{\ell }}_{str}{)}^2<1$ provides a laboratory for the study of holography in which both sides of AdS/CFT duality are under fairly good control. Worldsheet string theory is solvable, and for closed strings the dual spacetime CFT is a deformation of a symmetric product orbifold. Here we extend this construction to include open strings by adding a probe D-string, described semi-classically by an $Ad{S}_2$ D-brane in $Ad{S}_3$. The dual defect or boundary conformal field theory (BCFT) is again a deformed symmetric product, which now describes the Fock space of long open and closed strings near the AdS boundary, with a boundary deformation implementing the open/closed transition in addition to the symmetric product ${\mathbb{Z}}_2$ twist deformation that implements closed string joining/splitting. The construction thus provides an explicit example of an $Ad{S}_3\mathrm{/}BCF{T}_2$ duality.