CP(N) model on regions with boundary

TL;DR

This paper analyzes the CP(N) model in the large N limit on disc and annulus geometries with different boundary conditions, revealing that homogeneous condensates are not saddle points and discussing inhomogeneous condensate behavior near boundaries.

Contribution

It provides a detailed saddle point analysis of the CP(N) model on bounded regions with various boundary conditions, highlighting the non-existence of homogeneous condensates as saddle points.

Findings

Homogeneous condensate is not a saddle point in any considered boundary condition.

Inhomogeneous condensate behavior near boundaries is briefly characterized.

Analysis is performed in the large N limit using saddle point approximation.

Abstract

In this note we discuss the CP(N) model in large N limit in saddle point approximation on disc and annulus with various combinations of Dirichlet and Neumann boundary conditions. We show that homogeneous condensate is not a saddle point in any of considered cases. Behavior of inhomogeneous condensate near boundary is briefly discussed.