Quantum Gravity as a Deformed Topological Quantum Field Theory

TL;DR

This paper explores how quantum gravity can be formulated as a deformed topological quantum field theory, incorporating matter fields and using spin foam formalism to connect topological and gravitational dynamics.

Contribution

It introduces a method to construct the generating functional for BF theories with sources, enabling a perturbative approach to quantum gravity with matter.

Findings

Path integral for gravity with matter derived as a perturbation of topological BF theory

Framework for incorporating fermionic matter into spin foam models

Lowest order path integral describes topological gravity coupled to matter

Abstract

It is known that the Einstein-Hilbert action with a positive cosmological constant can be represented as a perturbation of the SO(4,1) BF theory by a symmetry-breaking term quadratic in the B field. Introducing fermionic matter generates additional terms in the action which are polynomial in the tetrads and the spin connection. We describe how to construct the generating functional in the spin foam formalism for a generic BF theory when the sources for the B and the gauge field are present. This functional can be used to obtain a path integral for General Relativity with matter as a perturbative series whose the lowest order term is a path integral for a topological gravity coupled to matter.