Duality and Dimensional Reduction of 5D BF Theory

TL;DR

This paper demonstrates how a boundary in 5D BF theory induces a 4D gauge-invariant Lagrangian with duality relations, suggesting fermionic boundary degrees of freedom from a bosonic bulk, applicable to various dimensions.

Contribution

It introduces a method to derive 4D boundary theories from 5D BF theory using boundary conditions, revealing duality relations and potential fermionic boundary modes.

Findings

Boundary conditions lead to a unique 4D gauge-invariant Lagrangian.

Boundary duality relations suggest fermionic boundary degrees of freedom.

Method applicable to quantum field theories in arbitrary dimensions.

Abstract

A planar boundary introduced \`a la Symanzik in the 5D topological BF theory, with the only requirement of locality and power counting, allows to uniquely determine a gauge invariant, non topological 4D Lagrangian. The boundary condition on the bulk fields is interpreted as a duality relation for the boundary fields, in analogy with the fermionization duality which holds in the 3D case. This suggests that the 4D degrees of freedom might be fermionic, although starting from a bosonic bulk theory. The method we propose to dimensionally reduce a Quantum Field Theory and to identify the resulting degrees of freedom can be applied to a generic spacetime dimension.