Generalised Symmetries and Manifest Duality I: Flat Spacetime

TL;DR

This work presents a new, gauge-potential–based action for duality-invariant gauge theories that remains manifestly Lorentz-invariant, polynomial, and readily quantizable. Central to the construction is a harmonic higher-form symmetry that fixes the correct self-dual field-strength in terms of potentials, enabling a straightforward decoupling of a shadow sector and clean coupling to matter, including the Witten effect and minimal coupling. The framework unifies with Sen’s flux-based description via gauging the harmonic symmetry and extends naturally to general dimensions and non-Abelian gauge fields, with explicit development of QEMD in D=4, complete Feynman rules, and field-strength–based perturbation theory that matches previous results. Supersymmetric extensions and a general dimensional formulation are developed, indicating broad applicability to duality-invariant QFTs in flat spacetime and offering a robust platform for future gravity- and string-inspired generalizations.

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.

Figures (5)

• Figure 1: The surfaces $\mathcal{D}$ only has the constraint that it ends on the worldline of an electrically charged particle represented by the blue line. As it is deformed to a new surface $\mathcal{D}'$ while still attached to the same electric worldline, the action changes if there are magnetic worldlines represented by purple lines that are within the volume bounded by these two surfaces. Demanding the partition function remains unchanged leads directly to charge quantisation.
• Figure 2: Monopole surrounded by axion domain wall. The theta vacua inside the shell is vanishing but outside the shell is a non-zero constant.
• Figure 3: $s$ and $u$ channel diagrams at tree level
• Figure 4: 1-loop diagrams contributing to charge renormalisation.
• Figure 5: Photon-source vertex in field strength based perturbation theory is mathematically equal to the vertex in the new potential based formalism.