Modular Invariance as an Explanation for the Absence of Monopoles.

TL;DR

This paper proposes that modular invariance as a discrete gauge symmetry explains why monopoles are not observed, by allowing gauge fixings that eliminate monopoles from the theory.

Contribution

It introduces a modular-invariant formulation of electromagnetism and shows monopoles cannot be observed due to gauge choices enabled by modular invariance.

Findings

Monopoles can be gauged away using modular invariance.

Modular invariance constrains the electromagnetic Hamiltonian.

No monopoles arise with independent modular transformations at each point.

Abstract

It is shown that modular invariance provides a natural explanation for the absence of monopoles when assumed to be a discrete gauge symmetry. It follows that monopoles can not be seen because it is always possible to find a suitable gauge-fixing in which they are not present. This result relies upon an easy to prove but non-trivial property of the modular group. A modular-invariant formulation for the hamiltonian of the electromagnetism is given. No monopole arises if independent modular transformations are allowed at each point in space-time where point-like charges are present.