Factorization conjecture and the open/closed string correspondence

We present evidence for the factorization of the world-sheet path integrals for 2d conformal field theories on the disk into bulk and boundary contributions. This factorization is then used to reinterpret a shift in closed string backgrounds in terms of boundary deformations in background independent open string field theory. We give a proof of the factorization conjecture in the cases where the background is represented by WZW and related models.