Abstract
We continue the analysis started in a recent paper of the large-N two-dimensional \( \mathbb{C}{\mathrm{\mathbb{P}}}^{N-1} \) 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 \( \mathrm{\mathcal{E}} \) (x, Λ, 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 \( \mathrm{\mathcal{E}}\left(x,\varLambda,\ L\right)\to \frac{N}{4\pi }{\varLambda}^2 \) at large LΛ 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 LΛ → 0 and the “confined” phase of the standard \( \mathbb{C}{\mathrm{\mathbb{P}}}^{N-1} \) model in two dimensions for LΛ → ∞.
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Betti, A., Bolognesi, S., Gudnason, S.B. et al. Large-N \( \mathbb{C}{\mathrm{\mathbb{P}}}^{\mathrm{N}-1} \) sigma model on a finite interval and the renormalized string energy. J. High Energ. Phys. 2018, 106 (2018). https://doi.org/10.1007/JHEP01(2018)106
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DOI: https://doi.org/10.1007/JHEP01(2018)106