A quantum field theory of simplicial geometry and the emergence of spacetime

TL;DR

This paper advocates for a discrete quantum spacetime framework using Group Field Theories, proposing that continuum spacetime and gravity emerge as a condensed phase from fundamentally discrete quantum structures, approached through QFT methods.

Contribution

It introduces a condensed matter perspective to the emergence of spacetime from GFT, outlining a research program for realizing this emergence in concrete terms.

Findings

GFT as a candidate for quantum spacetime

Continuum spacetime as a condensed phase of GFT

Proposal to use QFT methods for emergence analysis

Abstract

We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding problem of the emergence of a continuum spacetime and of General Relativity from fundamentally discrete quantum structures should be tackled from a condensed matter perspective and using purely QFT methods, adapted to the GFT context. We outline the picture of continuum spacetime as a condensed phase of a GFT and a research programme aimed at realizing this picture in concrete terms.