An Interacting Geometry Model and Induced Gravity

TL;DR

This paper introduces a quantum gravity model based on topological principles where the energy-momentum tensor is a BRST anticommutator, leading to a dynamically induced mass scale and emergent gravitons as collective geometric excitations.

Contribution

It presents a novel topological quantum gravity framework with induced mass scales and emergent gravitons, connecting BRST cohomology and cobordism theory.

Findings

Mass scale is induced dynamically by gravitational instantons.

Low energy theory contains gravitons as geometric collective excitations.

Topological excitations form the basis of the quantum gravity model.

Abstract

We propose the theory of quantum gravity with interactions introduced by topological principle. The fundamental property of such a theory is that its energy-momentum tensor is an BRST anticommutator. Physical states are elements of BRST cohomology group. The model with only topological excitations, introduced recently by Witten is discussed from the point of view of induced gravity program. We find that the mass scale is induced dynamically by gravitational instantons. The low energy effective theory has gravitons, which occur as the collective excitations of geometry, when the metric becomes dynamical. Applications of cobordism theory to QG are discussed.