Abstract
We derive the asymptotic symmetries of the manifestly duality invariant formulation of electromagnetism in Minkoswki space. We show that the action is invariant under two algebras of angle-dependent u(1) transformations, one electric and the other magnetic. As in the standard electric formulation, Lorentz invariance requires the addition of additional boundary degrees of freedom at infinity, found here to be of both electric and magnetic types. A notable feature of this duality symmetric formulation, which we comment upon, is that the on-shell values of the zero modes of the gauge generators are equal to only half of the electric and magnetic fluxes (the other half is brought in by Dirac- string type contributions). Another notable feature is the absence of central extension in the angle-dependent u(1)2-algebra.
Highlights
A notable feature of this duality symmetric formulation, which we comment upon, is that the on-shell values of the zero modes of the gauge generators are equal to only half of the electric and magnetic fluxes
Another notable feature is the absence of central extension in the angle-dependent u(1)2-algebra
There exists a formulation of electromagnetism in which electric-magnetic duality, which is always a symmetry of the action [14], is manifest
Summary
Are the “magnetic fields” (B1i is the standard electric field, while B2i is the standard magnetic field [14, 17] — up to signs that depend on conventions). These correspond precisely to proper gauge transformations (see subsection 2.4 below). These are the only vector field with this property: setting X = (αia), one finds. The dV Abk are independent 1forms, and so, the bulk term vanishes if and only if the coefficient ∂[iαja]vanishes. The surface term can be rewritten as −(1/2) S∞ d2Si ab ijkdV (∂jAak)αb, which vanishes only if the αb’s tend to a constant at infinity, i.e., if the functions αa on the 2-sphere reduce to their 0-th spherical harmonic, αa(θ, φ) = αa0.
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