Discrete gravity as a topological field theory with light-like curvature defects

TL;DR

This paper introduces a discrete gravity model formulated as a topological gauge theory with null surface defects, capturing curvature propagating at light speed, relevant for non-perturbative quantum gravity approaches.

Contribution

It presents a novel discrete gravity framework with light-like curvature defects using topological gauge theory, connecting to loop quantum gravity variables.

Findings

The model has no local degrees of freedom except at null surface defects.

The variables include spinors and surface densities coupled to a topological bulk theory.

Potential relevance for non-perturbative quantum gravity approaches.

Abstract

I present a model of discrete gravity, which is formulated in terms of a topological gauge theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a number of colliding null surfaces, which represent a system of curvature defects propagating at the speed of light. The underlying action is local and it is studied in both its Lagrangian and Hamiltonian formulation. The canonically conjugate variables on the null surfaces are a spinor and a spinor-valued two-surface density, which are coupled to a topological field theory for the Lorentz connection in the bulk. I discuss the relevance of the model for non-perturbative approaches to quantum gravity, such as loop quantum gravity, where similar variables have recently appeared as well.