Wilson lines and Ishibashi states in AdS₃/CFT₂

We provide a refined interpretation of a gravitational Wilson line in AdS₃ in terms of Ishibashi states in the dual CFT₂. Our strategy is to give a method to evaluate the Wilson line that accounts for all the information contained in the representation, and clarify the role of boundary conditions at the endpoints of the line operator. This gives a novel way to explore and reconstruct the local bulk dynamics which we discuss. We also compare our findings with other interpretations of Ishibashi states in AdS₃/CFT₂.