Topological Structure of Infrared QCD

TL;DR

This work proposes that the infrared sector of QCD forms a topological phase encoded in quantized Berry phases of slow soft-gauge configurations, replacing spacetime with the functional space $\mathcal{A}/\mathcal{G}$. By introducing two commuting Berry connections, $\mathcal{A}_F$ and $\mathcal{A}_G$, the dressed states are described by holonomies $\\mathcal{U}_C = \\mathcal{P}\\exp(i\\oint_C (\\mathcal{A}_F + \\mathcal{A}_G))$, yielding a discretized, gauge-invariant infrared structure and topological superselection sectors. The authors construct color-neutral hadronic states—$\pi^0$, the proton, tetraquark, and pentaquark—as topological composites of quantized infrared fluxes, illustrating how confinement-like behavior can emerge from topology rather than potentials. They discuss links to asymptotic symmetries and memory effects and provide a Dirac-monopole toy model to illustrate topological dressing, offering a geometrical reinterpretation of infrared dressing with potential implications for hadron spectroscopy and nonperturbative QCD. The framework reframes confinement and hadron structure as manifestations of topology in the space of gauge configurations, rather than solely as dynamical confinement in spacetime.

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.