# Casimir Effect and parallel $D$-Branes

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.

• Out of curiosity, why string field theory? Mar 18, 2021 at 13:13
• @NiharKarve Isn't string field theory the natural habitat for such a question? Mar 18, 2021 at 15:12
• I mean, string theory has D-branes and spacetime fields as well. Restricting to string field theory unnecessarily reduces the potential answerer pool for this question by a huge amount. Mar 18, 2021 at 15:16
• @NiharKarve OK, now I understand your point. Excuse my ignorance, but how does introducing another tag reduce the answerer pool? Shouldn't it increase the number, if the tag is related that is. Mar 18, 2021 at 15:19
• The string field theory formalism of string theory is a lot more difficult and much less well-known than the "standard" formulation of string theory that is presented first. Remember that "string field theory" $\ne$ "fields in string theory" (which is what I assume you were going for there) Mar 18, 2021 at 15:35

• OK $D$-branes have open strings stretched between them, but what about string interacting with $D$-branes. Consider a scenario where a closed string is scatterred of from a $D$-brane. Mar 18, 2021 at 15:44