Non-perturbative corrections to the Casimir energy for a scalar field theory with non-linear boundary conditions

We consider the case of a free real massive bulk scalar in D=4 dimensions, and embed two parallel plates as interfaces on which we impose non-linear boundary conditions, either Dirichlet- or Neumann-like, parameterized by a new coupling constant g. This mimics a non-Abelian gauge theory supplemented with boundary conditions on surfaces embedded in the bulk. We present the first evidence for a non-perturbative 1/g^2 boundary mass generation and its ensuing correction to the standard Casimir energy. This becomes possible by incorporating dynamical corrections to the effective boundary fields, which are used to build in the boundary conditions directly at the action level.