The generalized master fields

TL;DR

This paper introduces generalized master fields called free planar Markovian holonomy fields, extending the classical master field concept by allowing more general laws for simple loops, and establishes their connection to large N limits of Markovian holonomy fields.

Contribution

It constructs and analyzes free planar Markovian holonomy fields as generalized master fields, linking them to large N limits of Markovian holonomy fields with unitary groups.

Findings

Free planar Markovian holonomy fields can be realized as large N limits.

These fields generalize the classical master field by allowing more flexible loop laws.

The paper establishes a connection between free fields and Markovian holonomy fields.

Abstract

The master field is the large $N$ limit of the Yang-Mills measure on the Euclidean plane. It can be viewed as a non-commutative process indexed by paths on the plane. We construct and study generalized master fields, called free planar Markovian holonomy fields, which are versions of the master field where the law of a simple loop can be as more general as it is possible. We prove that those free planar Markovian holonomy fields can be seen as well as the large $N$ limit of some Markovian holonomy fields on the plane with unitary structure group.