Abstract
We consider a free topological model in 5D euclidean flat spacetime, built from two rank-2 tensor fields. Despite the fact that the bulk of the model does not have any particular physical interpretation, on its 4D planar edge nontrivial gauge field theories are recovered, whose features are entirely determined by the gauge and discrete symmetries of the bulk. In particular no 4D dynamics can be obtained without imposing a Time Reversal invariance in the bulk. Remarkably, one of the two possible edge models selected by the Time Reversal symmetries displays a true electromagnetic duality, which relates strong and weak coupling regimes. Moreover this same model, when considered on-shell, coincides with the Maxwell theory, which therefore can be thought of as a 4D boundary theory of a seemingly harmless 5D topological model.
Highlights
This is exactly what we stated above: the boundary fields and the boundary actions are determined by the broken Ward identities, and we anticipate that it will turn out that the gauge models which we will find on the 4D boundary are identified by discrete symmetries in the bulk
It is apparent that the discrete symmetries (3.9) and (3.10) play a striking role, since they select the edge dynamics: 4D boundary actions are possible only if one of the two TR symmetries are requested in the bulk
In this paper we considered the topological 5D action whose physical content is entirely confined on its 4D boundary, realized here by means of the θ- function appearing in (6.1)
Summary
In absence of a boundary, we consider the following bulk action depending on two rank-2 tensor fields Bμν and Cμν, built in the 5D flat Euclidean spacetime:. The gauge symmetries of the bulk action are broken by the boundary. Is the most general boundary term, compatible with locality and power counting, depending on five constant real parameters ai, which will turn out to be constrained by the symmetries of the model. This would trivialize the physics on the boundary, which instead is what we are looking for This is even more true in our case, since we are considering a topological field theory in the bulk, which lacks of local observables and physical degrees of freedom. Imposing the discrete symmetries T1(2) on the boundary action Sbd (2.22), yields the constraints on the parameters ai listed in the table
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