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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2502.11819 |
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| _version_ | 1866908441412370432 |
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| author | Gamboa, Jorge |
| author_facet | Gamboa, Jorge |
| contents | We investigate the emergence of geometric phases in chiral transformations within gauge theories coupled to fermions. We begin by analyzing the Schwinger model in (1+1) dimensions, where chiral symmetry is explicitly modified due to the dynamical generation of a photon mass. This model provides a controlled setting to study the interplay between anomalies and vacuum structure.
Building on these insights, we extend our analysis to four-dimensional QED by promoting the vacuum angle $θ$ to a dynamical field $θ(x)$. This generalization allows us to explore how the axial anomaly and the presence of a nontrivial vacuum structure modify the conventional chiral symmetry.
Using the adiabatic approximation, we demonstrate that chiral transformations are modified by the emergence of a nontrivial Berry phase, which introduces a geometric correction that depends on the topological properties of the vacuum. This result suggests that chiral transformations acquire an effective gauge structure in parameter space, in the presence of a dynamical $θ(x)$ field, leading to new physical consequences at low energies.
This framework establishes a novel connection between chiral symmetries, anomalies, and geometric phases, offering a unified approach to describing topological effects, vacuum structure, and infrared modifications in gauge theories with fermions. Moreover, our results suggest that Berry phases play a crucial role in the infrared structure of QED, potentially providing a mechanism for regularizing infrared divergences in theories with axial anomalies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement and Effective Field Theories Gamboa, Jorge High Energy Physics - Theory We investigate the emergence of geometric phases in chiral transformations within gauge theories coupled to fermions. We begin by analyzing the Schwinger model in (1+1) dimensions, where chiral symmetry is explicitly modified due to the dynamical generation of a photon mass. This model provides a controlled setting to study the interplay between anomalies and vacuum structure. Building on these insights, we extend our analysis to four-dimensional QED by promoting the vacuum angle $θ$ to a dynamical field $θ(x)$. This generalization allows us to explore how the axial anomaly and the presence of a nontrivial vacuum structure modify the conventional chiral symmetry. Using the adiabatic approximation, we demonstrate that chiral transformations are modified by the emergence of a nontrivial Berry phase, which introduces a geometric correction that depends on the topological properties of the vacuum. This result suggests that chiral transformations acquire an effective gauge structure in parameter space, in the presence of a dynamical $θ(x)$ field, leading to new physical consequences at low energies. This framework establishes a novel connection between chiral symmetries, anomalies, and geometric phases, offering a unified approach to describing topological effects, vacuum structure, and infrared modifications in gauge theories with fermions. Moreover, our results suggest that Berry phases play a crucial role in the infrared structure of QED, potentially providing a mechanism for regularizing infrared divergences in theories with axial anomalies. |
| title | Entanglement and Effective Field Theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.11819 |