Electromagnetic duality and central charge from first order formulation

TL;DR

This paper explores dual magnetic charges in p-form theories through a first order BF formulation, revealing their origin from reducible gauge symmetries and their relation to the current algebra of charges.

Contribution

It introduces a new perspective on dual magnetic charges as arising from reducible gauge symmetries in a BF theory framework, linking them to topological zero-modes.

Findings

Dual magnetic charges originate from reducible gauge symmetries.

Zero-modes in BF theory correspond to non-trivial dual charges.

The current algebra of charges extends naturally from BF theory to p-form theories.

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.