The Master Field of QCD$_2$ and the 'T Hooft Equation

TL;DR

This paper reformulates two-dimensional QCD in terms of a bilocal mesonic field, deriving the master field and showing that fluctuations satisfy the 't Hooft meson equation, providing a new perspective on the theory's large-N limit.

Contribution

It introduces a bilocal field formalism for QCD$_2$, explicitly constructs the master field, and connects fluctuations to the 't Hooft meson equation, offering a novel approach to analyze the theory.

Findings

Master field identified with the vacuum expectation value of the bilocal field.

Fluctuation equations match the 't Hooft meson equation.

Simplifies the $1/N$ expansion via saddle point technique.

Abstract

We rewrite the action for $QCD_2$ in the light cone gauge only in terms of a bilocal mesonic field. In this formalism the $1/N$ expansion can be done in a straightforward way by a saddle point technique that determines the master field to be identified with the vacuum expectation value of the bilocal field. Finally we show that the equation of motion for the fluctuations around the master field is identical with the 't Hooft meson equation.