Fermions on tori in uniform abelian fields

TL;DR

This paper explores the behavior of Fermi fields on tori with uniform abelian gauge backgrounds, revealing a duality that reduces the effective dimensionality of the field space, with implications for lattice regularization.

Contribution

It introduces a dual description of fermionic fields on tori in uniform abelian fields, reducing the dimensionality and connecting continuum and lattice formulations.

Findings

Duality between 2k-dimensional and k-dimensional field descriptions

Dimensional reduction is natural for uniform abelian backgrounds

Lattice regularization induces infrared regularization in lower dimensions

Abstract

We study Fermi fields defined on tori in the presence of gauge backgrounds carrying non-trivial topology. We show that 2k dimensional field space can alternatively be described by fields over a k-dimensional space. This dual description is particularly natural when the background is uniform and abelian. The reduction in number of dimensions carries over to the lattice. The lattice ultraviolet regularization induces an infrared regularization of the lower dimensional representations. We focus on k=1,2.