Electromagnetic Duality and Central Charge from First Order Formulation

Marc Geiller; Puttarak Jai-akson; Abdulmajid Osumanu; Daniele Pranzetti

Abstract

In the context of the infrared triangle there have been recent discussions on the existence and the role of dual charges. We present a new viewpoint on dual magnetic charges in p-form theories, and argue that they can be inherited from the charges of a first order formulation as a topological BF theory with potential. This happens because, depending on the spacetime dimension and on the form degree, the so-called translational gauge symmetries of BF theory become reducible and therefore admit zero-modes. Although such zero-modes lead to trivial symmetries of the p-form theory, they are associated with non-trivial charges. These turn out to be precisely the dual magnetic charges. The centrally-extended current algebra of electric and magnetic charges in the p-form theory then descends naturally from that of BF theory. This is an effort towards finding an existence criterion for dual charges.

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