In the well-known setup for the calculation of the Casimir effect, we take 2 perfectly reflecting plates, impose the appropriate boundary conditions on the relevant fields (scalar, vector, etc.) and calculate the energy of this configuration.
So the most natural analog of plates (that is objects that impose boundary conditions on fields) in String Theory are $D$-Branes. This got me wondering whether a similar scenario can be realized in String Theory where we consider the energy of an open or closed string field theory interacting with 2 parallel $D$-Branes.
The scenario I had in mind is loosely related to figure1. in Scattering of Strings from $D$-branes. I know that $D$-branes have open strings stretched between them, but that scenario would not be analogous to the Casimir effect setting because there is no propagation.