Gravity From Topological Field Theory

TL;DR

This paper develops a topological field theory that extends BF theories to include topological matter and generalizes a 3D gravity model to higher dimensions, revealing solutions like black holes in 4D.

Contribution

It introduces a new topological field theory framework that unifies and extends previous models of gravity and topological matter across various dimensions.

Findings

Models gravity as a topological field theory with matter coupling

Generalizes 3D gravity models to arbitrary dimensions

Finds constant curvature black hole solutions in 4D

Abstract

We construct a topological field theory which, on the one hand, generalizes BF theories in that there is non-trivial coupling to `topological matter fields'; and, on the other, generalizes the three-dimensional model of Carlip and Gegenberg to arbitrary dimensional manifolds. Like the three dimensional model, the theory can be considered to describe a gravitational field interacting with topological matter. In particular, in two dimensions, the model is that of gravity on a torus. In four dimensions, the model is shown to admit constant curvature black hole solutions.