Year: 2026
Type: preprint
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 $SL(2,\mathbb{Q})$ 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7221871323