Half dualization and non-invertible particle-vortex duality defect on lattice
arXiv:2607.13138
The paper introduces a method called half dualization that creates non‑invertible duality defects by applying a duality transformation only on a subregion of a lattice system, and demonstrates this in (2+1)‑dimensional XY models and their Zₙ‑gauged versions.
Abstract
We introduce half dualization as a general principle to construct non-invertible duality defects. The construction performs a duality transformation only in a subregion of spacetime, leaving an interface between the original theory and its dual. A non-invertible duality defect can be hosted on this interface. Half dualization is applicable whenever a local duality transformation is available, and does not depend on the spacetime dimension. We demonstrate the construction procedure in the (2+1)-dimensional Villainized charge- XY model on a cubic lattice. Half dualization yields a non-invertible particle-vortex duality defect whose fusion with its orientation reverse produces a (1+1)-dimensional gauge theory on the fusion surface. We then apply half dualization to the -gauged XY model relevant to the 3D XY transition. In the gauged model, the half dualization interface hosts a gauge covariant duality wall, rather than a genuine gauge invariant duality defect. It flows to an invertible duality defect in infrared when the gauge theory is confined or Higgsed.
6.5 pages