3d Abelian Dualities with Boundaries

TL;DR

This paper extends 3D Abelian dualities, including bosonization and particle-vortex duality, to scenarios with boundaries, confirming the approach through lattice realizations and ensuring boundary theories are anomaly-free.

Contribution

It introduces a method to implement 3D Abelian dualities with boundaries, maintaining consistency and anomaly cancellation, supported by lattice model verification.

Findings

Dualities are consistent with boundaries and anomalies are canceled.

Lattice models confirm the validity of the duality with boundaries.

Boundary theories support non-anomalous two-dimensional dynamics.

Abstract

We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the duality in terms of a Euclidean lattice.