3D Dynamics of 4D Topological BF Theory With Boundary

Abstract

We consider the four dimensional abelian topological BF theory with a planar boundary introduced following the Symanzik's method. We find the most general boundary conditions compatible with the fields equations broken by the boundary. The residual gauge invariance is described by means of two Ward identities which generate an algebra of conserved currents. We interpret this algebra as canonical commutation relations of fields, which we use to construct a three dimensional Lagrangian. As a remarkable by-product, the (unique) boundary condition which we found, can be read as a duality relation between 3D dynamical variables.

22 pages, no figures, version to appear on New Journal of Physics

References in corpus (3)

• The Quantum Spin Hall Effect: Theory and Experiment
• Tunneling between helical edge states through extended contacts
• Symanzik's Method Applied To The Fractional Quantum Hall Edge States

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