On Baryon Number Non-Conservation in Two-Dimensional O(2N+1) QCD

TL;DR

This paper models the large N limit of 2D O(2N+1) QCD using an infinite-dimensional Grassmannian, revealing baryon number as a topological quantity conserved modulo 2 and connecting it to matrix model master fields.

Contribution

It introduces a classical dynamical system on an infinite-dimensional Grassmannian to represent 2D O(2N+1) QCD at large N, highlighting novel topological properties of baryon number.

Findings

Baryon number is conserved only modulo 2.

The phase space is an infinite-dimensional Grassmannian.

Connection established between the model and matrix model master fields.

Abstract

We construct a classical dynamical system whose phase space is a certain infinite-dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O(2N+1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.