Large-N CPN-1 sigma model on a finite interval and the renormalized string energy

We continue the analysis started in a recent paper of the large-N two-dimensional CPN-1 sigma model, de fi ned on a fi nite space interval L with Dirichlet (or Neumann) boundary conditions. Here we focus our attention on the problem of the renormalized energy density epsilon (x, Lambda, L) which is found to be a sum of two terms, a constant term coming from the sum over modes, and a term proportional to the mass gap. The approach to epsilon(x, Lambda, L) -> N/4 4 pi Lambda(2) at large L Lambda is shown, both analytically and numerically, to be exponential: no power corrections are present and in particular no Luscher term appears. This is consistent with the earlier result which states that the system has a unique massive phase, which interpolates smoothly between the classical weakly-coupled limit for L Lambda -> 0 and the "confined" phase of the standard CPN-1 model in two dimensions for L Lambda -> infinity