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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.00078 |
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Table of Contents:
- We revisit the origin of the vacuum angle $θ$ in QCD using the adiabatic approximation combined with Fujikawa's method. By implementing a local chiral transformation and selecting a constant parameter $α(x) = θ$, we show that the QCD $θ$-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 $Δα$, 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.