Large-NP N − 1 sigma model on a finite interval

  • Stefano Bolognesi
  • Kenichi Konishi
  • Keisuke Ohashi
Open Access
Regular Article - Theoretical Physics


We analyze the two-dimensional ℂP N − 1 sigma model defined on a finite space interval L, with various boundary conditions, in the large N limit. With the Dirichlet boundary condition at the both ends, we show that the system has a unique phase, which smoothly approaches in the large L limit the standard 2DP N − 1 sigma model in confinement phase, with a constant mass generated for the n i fields. We study the full functional saddle-point equations for finite L, and solve them numerically. The latter reduces to the well-known gap equation in the large L limit. It is found that the solution satisfies actually both the Dirichlet and Neumann conditions.


1/N Expansion Sigma Models Solitons Monopoles and Instantons 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Stefano Bolognesi
    • 1
    • 2
  • Kenichi Konishi
    • 1
    • 2
  • Keisuke Ohashi
    • 1
    • 2
    • 3
  1. 1.Department of Physics “E. Fermi”University of PisaPisaItaly
  2. 2.INFN — Sezione di PisaPisaItaly
  3. 3.Osaka City University Advanced Mathematical InstituteOsakaJapan

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