# Topologically protected duality on the boundary of Maxwell-BF theory

## TL;DR

This paper investigates the boundary physics of Maxwell-BF theory in four dimensions, revealing a duality between boundary scalar and vector fields and the impact of topological terms on boundary degrees of freedom.

## Contribution

It identifies boundary degrees of freedom as dual scalar and vector fields and uncovers a strong-weak coupling duality in the boundary theory of Maxwell-BF.

## Key findings

- Boundary conditions and boundary current algebra derived
- Boundary degrees of freedom are a scalar and a vector field related by duality
- A strong-weak coupling duality separates different boundary regimes

## Abstract

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. The role of the Maxwell term in the bulk action is discussed, together with the relevance of the topological nature of the bulk action for the boundary physics.