Monopole-Fermion Scattering from Twisted Conformal Boundary States
Abstract
We derive monopole-fermion scattering correlators from conformal boundary states in twisted sectors. The key ingredient is that symmetry-preserving boundary conditions contain sectors twisted by topological symmetry lines. Their overlaps determine correlators of operators attached to these lines, including the outgoing excitations required by charge conservation in the Callan-Rubakov effect. We construct the twisted boundary states of N free Dirac fermions with U(1)N-preserving boundary conditions, extending the familiar description in terms of charge lattices to shifted lattices describing twisted sectors. Using cluster decomposition and open-closed duality, we determine their coefficients and fix their normalization relative to the untwisted boundary state. We find that the Callan-Rubakov boundary condition yields a two-point function between an incoming fermion and an outgoing defect operator with a coefficient of unit modulus, even when the corresponding correlators of ordinary local fermions vanish. Finally, we relate these correlators to four-dimensional partial-wave scattering using gauge-covariant asymptotic states. We identify the missing s-wave contribution to the unitarity relation and argue that the twisted channel supplies it with precisely the required normalization.
Related
- Spherical-DAHA predictions for boundary monopole bubbling of non-minuscule 't Hooft lines in 𝒩=4 SYM
- Separation of variables for non-diagonalisable models: XXX with twisted boundary conditions
- Conformal Scattering of Maxwell Potentials
- Rigidity of Lagrangian submanifolds with conformal Maslov form and Legendrian capillary boundary
- Conformal boundary rigidity for simple Finsler metrics
BibTeX
@misc{cordova2026monopolefermion,
title = {{Monopole-Fermion Scattering from Twisted Conformal Boundary States}},
author = {Clay Córdova and Diego García-Sepúlveda and Lian-Tao Wang and Yen-Chieh Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40779},
eprint = {2610.40779},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40779},
}
RIS
TY - UNPB
TI - Monopole-Fermion Scattering from Twisted Conformal Boundary States
AU - Clay Córdova
AU - Diego García-Sepúlveda
AU - Lian-Tao Wang
AU - Yen-Chieh Wang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40779
UR - https://arxiv.org/abs/2610.40779
AB - We derive monopole-fermion scattering correlators from conformal boundary states in twisted sectors. The key ingredient is that symmetry-preserving boundary conditions contain sectors twisted by topological symmetry lines. Their overlaps determine correlators of operators attached to these lines, including the outgoing excitations required by charge conservation in the Callan-Rubakov effect. We construct the twisted boundary states of N free Dirac fermions with U(1)^N-preserving boundary conditions, extending the familiar description in terms of charge lattices to shifted lattices describing twisted sectors. Using cluster decomposition and open-closed duality, we determine their coefficients and fix their normalization relative to the untwisted boundary state. We find that the Callan-Rubakov boundary condition yields a two-point function between an incoming fermion and an outgoing defect operator with a coefficient of unit modulus, even when the corresponding correlators of ordinary local fermions vanish. Finally, we relate these correlators to four-dimensional partial-wave scattering using gauge-covariant asymptotic states. We identify the missing s-wave contribution to the unitarity relation and argue that the twisted channel supplies it with precisely the required normalization.
ER -