A Concentration of Measure Phenomenon in the Principal Chiral Model

TL;DR

This paper applies the concentration of measure phenomenon to analyze the large N limit of the O(N) principal chiral model, showing the partition function converges to that of a free massive theory.

Contribution

It demonstrates the use of measure concentration to understand the large N behavior of the principal chiral model, revealing a free massive theory limit.

Findings

Partition function in large N limit is that of a free massive theory.

Concentration of measure phenomenon is effectively utilized in the analysis.

Provides insight into the asymptotic behavior of the model.

Abstract

We utilize the concentration of measure phenomenon to study the large $N$ limit of the $O(N)$ principal chiral model. The partition function in this limit is demonstrated to be that of a free massive theory.