On the effective Lagrangian of CP^(N-1) models in the large N limit

TL;DR

This paper derives the effective low energy Lagrangian for CP^{N-1} models in less than four dimensions using large N saddle point methods, with explicit results in two dimensions and potential applications.

Contribution

It provides a systematic derivation of the effective Lagrangian for CP^{N-1} models in the large N limit, including explicit two-dimensional results.

Findings

Explicit form of the effective Lagrangian in 2D

Method for constructing Lagrangian in d<4 dimensions

Discussion of potential applications

Abstract

The effective low energy Lagrangian of $CP^{N-1}$ models in $d < 4$ dimensions can be constructed in the large $N$ limit by solving the saddle point equations in the presence of a constant field strength. The two dimensional case is explicitly worked out and possible applications are briefly discussed.