Three-dimensional dynamics of four-dimensional topological BF theory with boundary. (English) Zbl 1448.81442
Summary: We consider the four-dimensional (4D) abelian topological BF theory with a planar boundary, following Symanzik’s method. We find the most general boundary conditions compatible with the field equations broken by the boundary. The residual gauge invariance is described by means of two Ward identities which generate a current algebra. We interpret this algebra as canonical commutation relations of fields, which we use to construct a 3D Lagrangian. As a remarkable by-product, we find a (unique) boundary condition which can be read as a duality relation between 3D dynamical variables.
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