Large N Limit on Langevin Equation: Two-Dimensional Nonlinear Sigma Model

TL;DR

This paper investigates the stochastic quantization of the two-dimensional nonlinear sigma model in the large N limit, showing that the effective Langevin equation reproduces known nonperturbative results from the path integral approach.

Contribution

It introduces an effective Langevin equation approach to analyze nonperturbative phenomena in the large N limit of the 2D nonlinear sigma model, aligning with traditional path integral results.

Findings

Effective Langevin equation reproduces path integral results

Nonperturbative phenomena analyzed in large N limit

Method bridges stochastic quantization and traditional approaches

Abstract

We study the stochastic quantization of two-dimensional nonlinear sigma model in the large $N$ limit. Our main tool is the {\it effective} Langevin equation with which we investigate nonperturbative phenomena and derive the results which are same as the path integral approach gives.