Edge Singularity in ``Induced QCD"

TL;DR

This paper investigates the behavior of the master field in induced QCD near its support edge, revealing a universal shape function and deriving a new equation for the meson spectrum, especially near one dimension.

Contribution

It introduces an extended scaling domain with a universal master field shape and derives a new explicit meson spectrum equation for induced QCD with general potentials.

Findings

Identified a universal shape function for the master field near the support edge.

Constructed the $D-1$-expansion for dimensions close to one.

Derived a new explicit equation for the meson spectrum.

Abstract

The behaviour of the master field in ``induced QCD" near the edge of its support is studied. An extended scaling domain, where the shape of the master field is a universal function, is found. This function is determined explicitly for the case of dimensions, close to one, and the $D-1$-expansion is constructed. The problem of the meson spectrum corresponding to this solution is analyzed. As a byproduct of these calculations, a new, explicit equation for the meson spectrum in ``induced QCD" with a general potential is derived.