Fermion−Monopole Scattering: A Unified Perspective
Abstract
We revisit the scattering of massless chiral fermions by a minimally charged BPS 't Hooft-Polyakov monopole. Existing proposals emphasize different aspects of this process and their connections are often unclear, giving rise to apparent conflicts concerning the outgoing states, energy conservation, and anomalous scattering amplitudes. We clarify the connection between different proposals within a common low-energy fermion-rotor description. Starting from the monopole background, we derive the rotor coupling and retain explicit fermion operators throughout the analysis. By adjoining a decoupled auxiliary scalar, we construct a dual theory that permits exact quantization. We show that the rotor vertex has a continuous spectral support down to zero energy and that its infrared exchange relations identify it as the twist dressing of the outgoing fermion. We also compute anomalous fermion correlators directly from fermion zero modes generated by winding configurations of the compact rotor. These results connect rotor dynamics, twisted outgoing states, and the zero-mode origin of anomalous correlators, resolving apparent conflicts and showing how the existing proposals fit into a mutually consistent picture within their common regime of applicability.
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BibTeX
@misc{geng2026fermionmonopole,
title = {{Fermion$\text-$Monopole Scattering: A Unified Perspective}},
author = {Hao Geng and Zekai Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07001},
eprint = {2611.07001},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07001},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fermion−Monopole Scattering: A Unified Perspective
AU - Hao Geng
AU - Zekai Wang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07001
UR - https://arxiv.org/abs/2611.07001
AB - We revisit the scattering of massless chiral fermions by a minimally charged BPS 't Hooft-Polyakov monopole. Existing proposals emphasize different aspects of this process and their connections are often unclear, giving rise to apparent conflicts concerning the outgoing states, energy conservation, and anomalous scattering amplitudes. We clarify the connection between different proposals within a common low-energy fermion-rotor description. Starting from the monopole background, we derive the rotor coupling and retain explicit fermion operators throughout the analysis. By adjoining a decoupled auxiliary scalar, we construct a dual theory that permits exact quantization. We show that the rotor vertex has a continuous spectral support down to zero energy and that its infrared exchange relations identify it as the twist dressing of the outgoing fermion. We also compute anomalous fermion correlators directly from fermion zero modes generated by winding configurations of the compact rotor. These results connect rotor dynamics, twisted outgoing states, and the zero-mode origin of anomalous correlators, resolving apparent conflicts and showing how the existing proposals fit into a mutually consistent picture within their common regime of applicability.
ER -