Arithmetic of Duality Defects in 4d Maxwell Theory
Abstract
We study the arithmetic structure of non-invertible duality defects in 4d U(1) Maxwell theory. First, we recast the problem of realizing an elliptic SL(2,ℚ) transformation as a duality defect in terms of complex multiplication for two-tori. The resulting classification includes well-studied cases in the literature, but extends to infinite Diophantine families of defects at a given gauge coupling. Second, we describe their worldvolume theories explicitly, with the Chern--Simons couplings determined by using continued fractions and tridiagonal continuant matrices. Third, we work out the fusion products of these defects, extracting the condensation defects and decoupled sectors both by lattice arithmetic and from the worldvolume descriptions. Finally, we illustrate our findings with the familiar N-ality defects (with N=2,3), but also give examples of infinite order.
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BibTeX
@misc{heisteeg2026arithmetic,
title = {{Arithmetic of Duality Defects in 4d Maxwell Theory}},
author = {Damian van de Heisteeg and Ling Lin and Giacomo Maggiorotti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18959},
eprint = {2610.18959},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18959},
}
RIS
TY - UNPB
TI - Arithmetic of Duality Defects in 4d Maxwell Theory
AU - Damian van de Heisteeg
AU - Ling Lin
AU - Giacomo Maggiorotti
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18959
UR - https://arxiv.org/abs/2610.18959
AB - We study the arithmetic structure of non-invertible duality defects in 4d U(1) Maxwell theory. First, we recast the problem of realizing an elliptic SL(2,ℚ) transformation as a duality defect in terms of complex multiplication for two-tori. The resulting classification includes well-studied cases in the literature, but extends to infinite Diophantine families of defects at a given gauge coupling. Second, we describe their worldvolume theories explicitly, with the Chern--Simons couplings determined by using continued fractions and tridiagonal continuant matrices. Third, we work out the fusion products of these defects, extracting the condensation defects and decoupled sectors both by lattice arithmetic and from the worldvolume descriptions. Finally, we illustrate our findings with the familiar N-ality defects (with N=2,3), but also give examples of infinite order.
ER -