Monopole scattering on the lattice

Speaker: Atsushi Ueda (Ghent University)
Series: Isaac Newton Institute Seminar Series
Note: MMBW03 - Structure of entanglement

What happens when a charged chiral fermion scatters off a magnetic monopole? This fundamental question underlies a longstanding puzzle in quantum field theory, with implications for the Standard Model. In Callan’s analysis, the outgoing state can appear to carry fractional fermion numbers, defying a description in terms of ordinary particles [1-3]. This difficulty, known as the “monopole paradox,” has challenged our understanding of fermion scattering for decades. Recent work offers a new perspective: the outgoing fermion is attached to a topological defect that ends on the monopole. The resulting state belongs to a twisted sector, providing a natural interpretation of its unconventional quantum numbers [4-6]. This serves as a compelling example in field theory. But what about on the lattice?

In this talk, I will first introduce examples from condensed matter physics. By joining two dual lattice theories through a suitably engineered duality defect, we can achieve perfect transmission of arbitrary wave packets. Although the interface is reflectionless, the transmitted excitation can look strikingly different from the incoming particle: it emerges dressed by a topological line. I will present a general and straightforward method for constructing such interfaces using matrix product unitaries [7]. I will then return to fermion–monopole scattering and discuss how these duality defects appear in lattice models of Andreev reflection [8] and SU(N) fermion–rotor dynamics[9].

[1] C. G. Callan, Jr., “Dyon-fermion dynamics,” Phys. Rev. D 26, 2058 (1982).

[2] V. A. Rubakov, “Adler-Bell-Jackiw anomaly and fermion number breaking in the presence of a magnetic monopole,” Nucl. Phys. B 203, 311–348 (1982).

[3] J. Polchinski, “Monopole catalysis: The fermion-rotor system,” Nucl. Phys. B 242, 345–363 (1984).

[4] M. van Beest, P. Boyle Smith, D. Delmastro, Z. Komargodski, and D. Tong, “Monopoles, scattering, and generalized symmetries,” JHEP 03 (2025) 014, arXiv:2306.07318.

[5] M. van Beest, P. Boyle Smith, D. Delmastro, R. Mouland, and D. Tong, “Fermion-monopole scattering in the Standard Model,” JHEP 08 (2024) 004, arXiv:2312.17746.

[6] V. Loladze, T. Okui, and D. Tong, “Dynamics of the fermion-rotor system,” JHEP 01 (2026) 052, arXiv:2508.21059.

[7] A. Ueda, V. Vander Linden, L. Lootens, J. Haegeman, P. Fendley, and F. Verstraete, “Perfect particle transmission through duality defects,” Nature Physics 22, 1684–1690 (2026), arXiv:2510.26780.

[8] A. Ueda, T. Numasawa, B. De Vos, and M. Watanabe, “Emergent Andreev Reflection from a Lattice Duality Defect,” Phys. Rev. Lett. 137, 146504 (2026), arXiv:2606.23684.

[9] L. Nagano, A. Ueda, F. Suzuki, A. Chou, and K. Terashi, in preparation.