The Role of Berry Phases in the QCD Vacuum Structure

TL;DR

This paper explores the geometric origin of the QCD vacuum angle using adiabatic approximation and Berry phases, providing a new perspective on topological aspects and anomalies in QCD.

Contribution

It introduces a non-perturbative interpretation of the QCD $ heta$-term through Berry phases and adiabatic gauge conditions, linking topology, anomalies, and vacuum structure.

Findings

QCD $ heta$-term arises from Berry phase considerations.

Topological information is encoded in the functional Berry phase.

Provides a geometric interpretation of the QCD vacuum structure.

Abstract

We revisit the origin of the vacuum angle $\theta$ in QCD using the adiabatic approximation combined with Fujikawa's method. By implementing a local chiral transformation and selecting a constant parameter $\alpha(x) = \theta$, we show that the QCD $\theta$-term emerges naturally in the effective action. This construction provides a non-perturbative interpretation of the axial anomaly and highlights the role of the adiabatic gauge condition in isolating the topological sector of the theory. As a consequence, the physical states acquire topological information encoded in the functional Berry phase $\Delta \alpha$, which manifests itself as a holonomy over the space of gauge configurations. This result offers a geometric and dynamical perspective on the structure of the QCD vacuum and its relation to anomaly-induced phases.