Grassmannian sigma model on a finite interval

TL;DR

This paper analyzes the phase structure of the two-dimensional Grassmannian sigma model on a finite interval, exploring boundary conditions and analytical solutions, revealing a phase structure similar to the $ ext{C}P(N)$ model.

Contribution

It provides a detailed study of boundary conditions and phase structure of the Grassmannian sigma model on a finite interval, extending understanding beyond the infinite case.

Findings

Identification of boundary conditions allowing analytical solutions

Discovery of a nontrivial phase structure on the interval

Similarity of phase structure to the $ ext{C}P(N)$ model

Abstract

We discuss the two-dimensional Grassmannian sigma model $\mathbb{G}_{N, M}$ on a finite interval $L$. The different boundary conditions which allow to obtain analytical solutions by the saddle-point method in the large $N$ limit are considered. The nontrivial phase structure of the model on the interval similar to $\mathbb{C}P(N)$ model is found.