The symmetry between electricity and magnetism and the structure of space and time" (Rosenblum Lecture):
The symmetry between electricity and magnetism (“electric-magnetic duality”) is reviewed for abelian p-form fields in different spacetime dimensions.
For those special ranks of the form and of the spacetime dimension for which the electric and magnetic representations are of the same type, electric-magnetic duality can be implemented as a symmetry of the action, and not just of the equations of motion. This can only be achieved at the price of giving up manifest Lorentz invariance. Thus one can have either manifest electric-magnetic duality invariance or manifest spacetime invariance; but not both. Furthermore, one can derive spacetime invariance from duality invariance. This shows a subtle interplay between both invariances, and suggests that it may be advantageous to look at electric-magnetic duality as more fundamental than spacetime structure, in order to unravel “hidden” properties of gauge theories. Extensions of the analysis to include supersymmetry, non-abelian gauge fields, and gravity are also touched upon. In all cases the need to double the number of gauge potentials is emphasized. Although sources do not play a central role in the discussion, the notion of “charged event”, which is a kind of source distinctly suggested by electric-magnetic duality, and different from a particle or a standard extended object, is brought in.