Abstract
A planar boundary introduced à la Symanzik in the 5D topological BF theory, with only the requirements 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.
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Notes
In a different context, this is the method proposed by Pauli and Villars in [12] to cure the U.V. divergencies in QFT.
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Amoretti, A., Blasi, A., Caruso, G. et al. Duality and dimensional reduction of 5D BF theory. Eur. Phys. J. C 73, 2461 (2013). https://doi.org/10.1140/epjc/s10052-013-2461-3
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DOI: https://doi.org/10.1140/epjc/s10052-013-2461-3