  We consider deformations of D-brane systems induced by a change in the closed
string background in the framework of bosonic open-closed string field theory,
where it is possible to unambiguously tame infrared divergences originating
from both open and closed string degenerations. A closed string classical
solution induces a tadpole for the open strings which shifts the open string
vacuum and generates a cosmological constant composed of two terms: one which
is directly related to the closed string solution and the other which depends
on the open string vacuum shift. We show that only the sum of these two terms
is invariant under closed SFT gauge transformations and therefore is an
observable. We conjecture that this observable is universally proportional to
the shift in the world-sheet disk partition function between the starting
D-brane in undeformed background and the final D-brane in deformed background,
which typically includes also a change in the string coupling constant. We test
the conjecture by considering a perturbative closed string solution describing
deformations of a Narain compactification and, from the SFT cosmological
constant, we reproduce the expected shift in the $g$-function of various
D-branes living in the compactification. In doing this we are also able to
identify a surprising change in the string coupling constant at second order in
the deformation.
