Topological Structure of Infrared QCD

TL;DR

This paper explores the infrared structure of QCD using a topological and geometric framework, revealing features akin to topological phases and proposing a novel perspective on confinement and hadronic states.

Contribution

It introduces a topological phase description of infrared QCD using Berry phases and gauge connection space, linking gauge topology with hadronic bound states.

Findings

Infrared QCD exhibits topological phase features.

Color-neutral states emerge as topological bound states.

The framework connects gauge topology with hadronic excitations.

Abstract

We investigate the infrared structure of QCD within the adiabatic approximation, where soft gluon configurations evolve slowly compared to the fermionic modes. In this formulation, the functional space of gauge connections replaces spacetime as the natural arena for the theory, and the long-distance behavior is encoded in quantized Berry phases associated with the infrared clouds. Our results suggest that the infrared sector of QCD exhibits features reminiscent of a \emph{topological phase}, similar to those encountered in condensed-matter systems, where topological protection replaces dynamical confinement at low energies. In this geometric framework, color-neutral composites such as quark--gluon and gluon--gluon clouds arise as topological bound states described by functional holonomies. Illustrative applications to hadronic excitations are discussed within this approach, including mesonic and baryonic examples. This perspective provides a unified picture of infrared dressing and topological quantization, establishing a natural bridge between non-Abelian gauge theory, adiabatic Berry phases, and the topology of the space of gauge configurations.