Generalised Symmetries and Manifest Duality I: Flat Spacetime

TL;DR

This paper introduces a new, Lorentz-invariant action for duality-symmetric gauge theories that simplifies quantization, extends to non-Abelian fields, and naturally incorporates matter coupling and supersymmetry.

Contribution

It provides a novel, manifestly Lorentz-invariant, polynomial action for duality-symmetric gauge theories that unifies and extends previous formalisms, including Sen's flux-based approach.

Findings

Reproduces flux-based description via gauging harmonic higher-form symmetry

Allows minimal coupling to matter and supersymmetrisation

Demonstrates derivation of self-dual Yang-Mills equations and charge quantisation

Abstract

We present a novel, manifestly Lorentz-invariant, polynomial, and straightforwardly quantisable action for duality-symmetric gauge theories formulated using gauge potentials. Central to our construction is the identification of a harmonic higher-form symmetry which uniquely determines the field-strength and resolves the tension between Bianchi identities and dynamical equations of motion. Gauging this symmetry reproduces the flux-based description due to Sen and shows that the quantum consistency checks established for Sen's formalism are automatically subsumed by our action. Unlike Sen's flux-based formalism, our framework admits a simple minimal coupling to matter, the Witten effect, and extends readily to non-Abelian gauge fields. The new action admits remarkably simple supersymmetrisation. Using this action, we derive self-dual Yang-Mills equations from first principles and demonstrate the formalism explicitly for quantum electro-magnetodynamics in $D=4$. We also present a proof of charge quantisation that applies equally to ours and Sen's formulations.