Large-N CP(N-1) sigma model on a finite interval and the renormalized string energy

Abstract

We continue the analysis started in a recent paper of the large-N two-dimensional CP(N-1) sigma model, defined on a finite space interval L with Dirichlet (or Neumann) boundary conditions. Here we focus our attention on the problem of the renormalized energy density $\mathcal{E}(x,\Lambda ,L)$ 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 $\mathcal{E}(x,\Lambda ,L)\to \frac{N}{4\pi }{\Lambda }^2$ at large $L\Lambda$ is shown, both analytically and numerically, to be exponential: no power corrections are present and in particular no Lüscher 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 $L\Lambda \to 0$ and the "confined" phase of the standard CP(N-1) model in two dimensions for $L\Lambda \to \infty$.

LaTeX: 32 pages, 11 figures; V2: appendices E and F added and typos corrected; V3: grant information added

References in corpus (1)

• Monopole-vortex complex at large distances and nonAbelian duality

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