The generalized master fields

Understand

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.