Casimir Force for the $\mathbb{C}{P}^{N-1}$ Model

In this work, we derive exact self-consistent solutions to the gap equations of the $\mathbb{C}{P}^{N-1}$ model on a finite interval with Dirichlet boundary conditions in the large-$N$ approximation. The solution reproduce the confining phase in the infinite system by taking the appropriate limit. We compute the vacuum energy and the Casimir force and observe that the sign of the force is always attractive.