  We study the Casimir force between defects (branes) of co-dimension larger
than 1 due to quantum fluctuations of a scalar field $\phi$ living in the bulk.
We show that the Casimir force is attractive and that it diverges as the
distance between the branes approaches a critical value $L_c$. Below this
critical distance $L_c$ the vacuum state $\phi=0$ of the theory is unstable,
due to the birth of a tachyon, and the field condenses.
