Even-dimensional topological gravity from Chern-Simons gravity

TL;DR

This paper demonstrates how even-dimensional topological gravity can be derived from a higher-dimensional Chern-Simons gravity theory, emphasizing the role of boundary dynamics and Poincare group symmetries.

Contribution

It establishes a connection between 2n-dimensional topological gravity and (2n+1)-dimensional Chern-Simons gravity, highlighting the boundary dynamics and coset field interpretation.

Findings

Topological gravity in even dimensions arises from boundary dynamics of higher-dimensional Chern-Simons theory.

The field  is identified with a coset field from Poincare group realizations.

The approach provides a gauge-invariant formulation of even-dimensional topological gravity.

Abstract

It is shown that the topological action for gravity in 2n-dimensions can be obtained from the 2n+1-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a 2n+1-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field $\phi^{a}$, which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d-1,1).