Topological gravity and transgression holography

Understand

We show that Poincare-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 Poincare group ISO(d-1,1).

• The resulting theory is a gauged WZW model whereby the transition functions relating gauge fields live in the coset ISO(d-1,1)/SO(d-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 Poincare group in three dimensions.