A simple model of dimensional collapse

TL;DR

This paper introduces a simple two-dimensional scalar field model interacting with geometry, demonstrating a collapse from two to one dimension depending on the parameter d, providing insights into quantum gravity interactions.

Contribution

It presents a minimal model capturing key features of conformal matter interacting with quantum gravity, highlighting dimensional collapse phenomena.

Findings

For d<0, the universe remains two-dimensional.

For d>0, the universe collapses to one dimension.

The model exhibits some characteristics of full quantum gravity theories.

Abstract

We consider a simple model of d families of scalar field interacting with geometry in two dimensions. The geometry is locally flat and has only global degrees of freedom. When d<0 the universe is locally two dimensional but for d>0 it collapses to a one dimensional manifold. The model has some, but not all, of the characteristics believed to be features of the full theory of conformal matter interacting with quantum gravity which has local geometric degrees of freedom.