Large-N ℂℙN − 1 sigma model on a finite interval: general Dirichlet boundary conditions

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


This is the third of the series of articles on the large-N two-dimensional ℂℙN − 1 sigma model, defined on a finite space interval L with Dirichlet boundary conditions. Here the cases of the general Dirichlet boundary conditions are studied, where the relative ℂℙN − 1 orientations at the two boundaries are generic, and numerical solutions are presented. Distinctive features of the ℂℙN − 1 sigma model, as compared e.g., to an O(N) model, which were not entirely evident in the basic properties studied in the first two articles in the large N limit, manifest themselves here. It is found that the total energy is minimized when the fields are aligned in the same direction at the two boundaries.


Effective Field Theories 1/N Expansion Nonperturbative Effects 


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) 2018

Authors and Affiliations

  • Stefano Bolognesi
    • 1
    • 2
  • Sven Bjarke Gudnason
    • 3
  • Kenichi Konishi
    • 1
    • 2
  • Keisuke Ohashi
    • 4
  1. 1.Department of Physics “E. Fermi”University of PisaPisaItaly
  2. 2.INFN, Sezione di PisaPisaItaly
  3. 3.Institute of Modern PhysicsChinese Academy of SciencesLanzhouChina
  4. 4.Research and Education Center for Natural SciencesKeio UniversityYokohamaJapan

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