# Electromagnetic Self-Duality in a Lattice Model

## TL;DR

This paper develops a lattice model of electric and magnetic charges demonstrating electromagnetic self-duality, with implications for quantum electrodynamics and monopole interactions, including potential continuum limits at the self-dual point.

## Contribution

It introduces a lattice theory with self-dual symmetry for electric and magnetic charges, analyzing radiative corrections and the possibility of a continuum limit at the self-dual point.

## Key findings

- Virtual electron and monopole loops contribute opposite sign corrections to the photon propagator.
- The model suggests a phase where QED coexists with strongly interacting monopoles and spontaneous chiral symmetry breaking.
- Discussion of potential continuum limit at the self-dual coupling point.

## Abstract

We formulate a Euclidean lattice theory of interacting elementary spin-half electric and magnetic charges, which we refer to as electrons and magnetic monopoles respectively. The model uses the polymer representation of the fermion determinant, and exhibits a self-dual symmetry provided electric charge $e$ and magnetic charge $g$ obey the minimal Dirac quantisation condition $eg=2\pi$. In a hopping parameter expansion at lowest order, we show that virtual electron and monopole loops contribute radiative corrections of opposite sign to the photon propagator. We argue that in the limit $e\to0$, fermion mass $\mu\to0$, the model describes QED together with strongly interacting monopoles whose chiral symmetry is spontaneously broken. Prospects for the existence of an interacting continuum limit at the self-dual point $e=g$ are discussed.