CP(N-1) model on finite interval in the large N limit

TL;DR

This paper analyzes the CP(N-1) sigma model on a finite interval using the 1/N expansion, revealing two phases separated by a phase transition at a critical interval length, and discusses the vacuum energy and Casimir effects.

Contribution

It provides a detailed analysis of the phase structure and vacuum energy dependence of the CP(N-1) model on finite intervals in the large N limit, including Casimir-type effects.

Findings

Two distinct phases separated by a phase transition at R ~ 1/Λ

Vacuum energy exhibits Casimir-type 1/R scaling

Phase transition impacts the model's vacuum structure

Abstract

The CP(N-1) \sigma\ model on finite interval of length R with Dirichlet boundary conditions is analysed in the 1/N expansion. The theory has two phases, separated by a phase transition at R ~ 1/\Lambda, \Lambda\ is dynamical scale of the CP(N-1) model. The vacuum energy dependence of R, and especially Casimir-type scaling 1/R, is discussed.