Topological gravity localization on a delta-function like Brane

TL;DR

This paper develops a topological gravity framework in a five-dimensional braneworld scenario with a delta-function like brane, connecting topological field theories to gravity in both bulk and brane regions, aiding quantum gravity research.

Contribution

It constructs a topological gravity model in a 5D braneworld with a delta-function brane, deriving the Palatini form of General Relativity in bulk and brane, advancing quantum gravity understanding.

Findings

Derived 5D topological gravity action with a delta-function brane.

Obtained Palatini form of GR in bulk and brane.

Provides a foundation for quantum gravity in braneworlds.

Abstract

Besides the String Theory context, the quantum General Relativity can be studied by the use of constrained topological field theories. In the celebrated Plebanski formalism, the constraints connecting topological field theories and gravity are imposed in space-times with trivial topology. In the braneworld context there are two distinct regions of the space-time, namely, the bulk and the braneworld volume. In this work we show how to construct topological gravity in a scenario containing one extra dimension and a delta-function like 3-brane which naturally emerges from a spontaneously broken discrete symmetry. Starting from a D=5 theory we obtain the action for General Relativity in the Palatini form in the bulk as well as in the braneworld volume. This result is important for future insights about quantum gravity in brane scenarios.