Topologically protected duality on the boundary of Maxwell-BF theory

Understand

The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four dimensional spacetime.

• The presence of a boundary breaks the Ward identities which describe the gauge symmetries of the theory, and, using standard methods of quantum field theory, the most general boundary conditions and a nontrivial current algebra on the boundary are derived.
• The electromagnetic structure which characterizes the boundary is used to identify the three dimensional degrees of freedom, which turn out to be formed by a scalar field and a vector field, related by a duality relation.
• The induced three dimensional theory shows a strong-weak coupling duality which separates different regimes described by different covariant actions.