Glue Condensate, Quark Condensate and Dirac Spectral Density

TL;DR

This paper derives a regularized formula linking glue and quark scalar densities via Dirac spectral density, clarifying their relation to symmetry breaking, IR phases, and UV-IR dynamics in QCD.

Contribution

It introduces a new regularized formula for the gluon condensate in terms of Dirac spectral density, enhancing understanding of nonperturbative QCD phenomena.

Findings

Provides a formula relating gluon and quark scalar densities

Clarifies the distinction between anomalous and spontaneous symmetry breaking

Explores the implications for UV and IR dynamics in QCD

Abstract

I derive the regularized formula for glue scalar density (gluon condensate) in terms of Dirac spectral density [arXiv:2509.03509], and elaborate on its uses and meaning. Particular attention is given to understanding of what this new formula reveals about the relation between glue and quark scalar densities, how it relates to IR phase, how it clarifies the distinction between anomalous and spontaneous ways of breaking symmetries, and what it says about the relation between UV and IR in QCD.