Towards coarse graining of discrete Lorentzian quantum gravity

TL;DR

This paper introduces a method for coarse graining in Lorentzian causal set quantum gravity using a matrix-model approach and a flow equation for the effective action, advancing the understanding of scale in discrete quantum gravity.

Contribution

It presents the first step towards implementing coarse graining in Lorentzian causal set quantum gravity through a novel matrix-model formulation and flow equation approach.

Findings

Derived a flow equation for the effective action in causal set quantum gravity.

Established a matrix-model-like language for the space of actions.

Proposed an abstract notion of scale based on counting discrete elements.

Abstract

A first step towards implementing a notion of coarse graining in an intrinsically Lorentzian, discrete quantum- gravity approach, namely causal set quantum gravity is taken. It makes use of an abstract notion of scale, based on counting the number of discrete elements. To that end, the space of actions for causal set quantum gravity is written in a matrix-model-like language, and a flow equation for the effective action of the model is derived from the path integral.