Can (Electric-Magnetic) Duality Be Gauged?

TL;DR

This paper investigates whether electric-magnetic duality in Maxwell theory can be promoted to a local gauge symmetry and concludes that, using standard methods, it cannot be gauged, impacting related theories like supergravity.

Contribution

It demonstrates that the Noether procedure cannot successfully gauge electric-magnetic duality in Maxwell theory, highlighting a fundamental limitation.

Findings

Gauging duality via the Noether procedure is not possible.

Electric-magnetic duality cannot be promoted to a local gauge symmetry.

Implications for supergravity and related theories are discussed.

Abstract

There exists a formulation of the Maxwell theory in terms of two vector potentials, one electric and one magnetic. The action is then manifestly invariant under electric-magnetic duality transformations, which are rotations in the two-dimensional internal space of the two potentials, and local. We ask the question: can duality be gauged? The only known and battled-tested method of accomplishing the gauging is the Noether procedure. In its decanted form, it amounts to turn on the coupling by deforming the abelian gauge group of the free theory, out of whose curvatures the action is built, into a non-abelian group which becomes the gauge group of the resulting theory. In this article, we show that the method cannot be successfully implemented for electric-magnetic duality. We thus conclude that, unless a radically new idea is introduced, electric-magnetic duality cannot be gauged. The implication of this result for supergravity is briefly discussed.