Quantum Duality in Electromagnetism and the Fine-Structure Constant

TL;DR

This paper explores how electric-magnetic duality and higher symmetries in Maxwell theory lead to non-invertible symmetries when the fine-structure constant is rational, revealing new quantum invariances with implications for boundary conditions and operator actions.

Contribution

It introduces and explicitly constructs non-invertible symmetries in Maxwell theory arising from electric-magnetic duality and discrete gauging, expanding understanding of quantum symmetries in electromagnetism.

Findings

Non-invertible symmetries exist when the fine-structure constant is rational.

These symmetries are realized as topological defects in the theory.

They influence boundary conditions and the structure of the Hilbert space.

Abstract

We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of electric-magnetic duality and gauging a discrete subgroup of the one-form global symmetry. These non-invertible symmetries are approximate quantum invariances of the natural world which emerge in the infrared below the mass scale of charged particles. We construct these symmetries explicitly as topological defects and illustrate their action on local and extended operators. We also describe their action on boundary conditions and illustrate some consequences of the symmetry for Hilbert spaces of the theory defined in finite volume.