Abstract
We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be straightforwardly imposed, leading to a simple formulation for theories with the SO(2) duality invariance. When specialized to the conformally invariant case, our construction provides a manifestly duality-symmetric formulation of the recently discovered ModMax theory. We briefly comment on a natural generalization of this approach to p-forms in 2p+2 dimensions.
Highlights
We briefly comment on a natural generalization of this approach to p-forms in 2p þ 2 dimensions
Fμν ≡ ∂μAν − ∂νAμ and the Hodge star is defined by ⋆Fμν 1⁄4 εμνσρFσρ=2, while most generally we view L as an arbitrary function
One may be interested in coupling this theory to both electrically and magnetically charged matter, as done for free theories in [16,17,18,19]
Summary
Theoretical Physics Group, Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom (Received 7 August 2021; accepted 8 November 2021; published 27 December 2021). We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be straightforwardly imposed, leading to a simple formulation for theories with the SO(2) duality invariance. When specialized to the conformally invariant case, our construction provides a manifestly duality-symmetric formulation of the recently discovered ModMax theory. We briefly comment on a natural generalization of this approach to p-forms in 2p þ 2 dimensions
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