Topological gravity and transgression holography

We show that Poincar\'e-invariant topological gravity in even dimensions can be formulated as a transgression field theory in one higher dimension whose gauge connections are associated to linear and nonlinear realizations of the Poincar\'e group $ISO(d\ensuremath{-}1,1)$. The resulting theory is a gauged Wess-Zumino-Witten (WZW) model whereby the transition functions relating gauge fields live in the coset $\frac{ISO(d\ensuremath{-}1,1)}{SO(d\ensuremath{-}1,1)}$. The coordinate parametrizing the coset space is identified with the scalar field in the adjoint representation of the gauge group of the even-dimensional topological gravity theory. The supersymmetric extension leads to topological supergravity in two dimensions starting from a transgression field theory which is invariant under the supersymmetric extension of the Poincar\'e group in three dimensions. We also apply this construction to a three-dimensional Chern-Simons theory of gravity which is invariant under the Maxwell algebra and obtain the corresponding WZW model.

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