Magnetic charges in local field theory

TL;DR

The paper develops a unified framework for electric and magnetic gaugings in four dimensions by introducing tensor fields and an embedding tensor, enabling a gauge invariant Lagrangian that accommodates both electric and magnetic charges without prior duality transformations. It constructs a universal vector-tensor Lagrangian with a topological term that preserves the correct degrees of freedom and shows how integrating out fields or gauge fixing yields equivalent formulations. The approach applies to flux compactifications and extends to N=2 supergravity, with explicit abelian and nonabelian gaugings described in a symplectically covariant way. Overall, it clarifies how electric-magnetic duality can be realized at the Lagrangian level and provides a versatile tool for building consistent gauged theories.

Abstract

Novel Lagrangians are discussed in which (non-abelian) electric and magnetic gauge fields appear on a par. To ensure that these Lagrangians describe the correct number of degrees of freedom, tensor gauge fields are included with corresponding gauge symmetries. Non-abelian gauge symmetries that involve both the electric and the magnetic gauge fields can then be realized at the level of a single gauge invariant Lagrangian, without the need of performing duality transformations prior to introducing the gauge couplings. The approach adopted, which was initially developed for gaugings of maximal supergravity, is particularly suited for the study of flux compactifications.